Word "Margam" means "way". Bharatanatyam performance comprises number of items performed in certain order.
During the times of Tanjore Quartette, dance concert was statred only after performing certain ritualisitc actions, such as playing drums on the stage (the practice was called Melarapti) and singing Todaya Mangalam songs (which were believed to of benedictory and purifying effect.) In our days, this practices are aither not followed, or folloed in some different way. The good example is Todaya Mangalam, which became a dance item itself and is performed now as invocatory item in some schools of Bharatanatyam (more information on Todaya Mangalam is available here: Other dance compositions.)
The word "Alarippu" means "blooming" (root "alaru" may be found in Telugu, Tamil and other Dravidian languages). Alarippu is short invocatory Nritta item. Purpose of Alarippu is paying obeisance or salutation to God, guru and audience. It opens performance and opens body for dance, the limbs are warmed up by simple movements, mind is focused by precise rhythm and emotions are activated by harmony and beauty of traditional choreography and inner joy of dance, so dear to each dancer.
Alarippu can be performed in different thalas and jatis, traditional alarrippus are rupaka, misra chapu and chaturasra eka thalam alarippu.
S Sharada Teacher explained Alarippu as follows:
"The Alarippu movements begin with the eyes and neck and move progressively downwards. This is essencially a dance dedicating each part of the body before commencing the actual program. Alarippu conveys happyness. "Nanadanti anena devata - iti naandi." That which makes the deva-s happy is naandi. Hence the Alarippu is like the naandi sloka.Hence the Alarippu is like the naandi sloka. Since this is dedicatory dance, it has to be simple, setting the stage for the more complicated dance to follow."
Before starting performance we need to create its atmosphere first. We need to create special time and space environment of dance. In Natya Shastra Bharata Muni said that dance is of divine origin, it connects higher worlds of Gods with the Earth.
Space of the stage becomes point of this connection for the period of performance where higher world enters casual reality and penetrates further through the hearts of people watching it.
Thus, it is important to arrange place and time properly. Simple and exact rhythm of Alarippu adjusts flow of time to the tempo of dance. Rhythm synchronizes heart beats of dancer, musicians and spectators.
Alarippu begins with eye movement. Eyes are very important elements of communication. To communicate people need to keep eye contact. Thus, dancer enters into contact with audience via eyes.
First set of movements is done in Sama pada, dancer points to different sides, as if indicating the space round and including the space itself into dance or inviting guardians of nine directions to participate and protect the stage.
Then dancer rises hands from Natya Ramba up with Anjali as if addressing the heavens. Then open in Natya Ramba again as if holding flow of heavenly Ganga.
Second set of adavus is performed in Muzhu mandi. Dancer lowers down to the Earth, as if seeking power and strength from it.
After salutation series of adavus are performed. As an artist draws a sketch or hieroglyphs using his brush, the dancer fills the space with dance movements in increasing tempo. Message of pure Nritta is beauty. Beauty enters the stage in final sequence of fast and precise adavus. Beauty arranges the space and opens performance.
Dancer retreats back as is bowing to the audience for attention, hands are flying from up downwards, as if heaven are open and wonderful stream of light falls on the place ready for being transmitted further, into auditorium...
This is pure Nritta item set to tune (ragam) in particular rhythm (thalam). Jathiswasram includes Jathi (sollukattu), Pallavi, Anupallavi and one or more Charanas. There are no any sahityam passages present, the whole composition is sung using swaras (solfa patterns).
Thus, Jathiswaram could be defined as "musical comosition without sahitya, which melody progressively becomes more comlex in sense of rhythm." 
The meaning of Nritta, pure dance, is using the God given body and limbs we create as many forms of beauty as possible through flow of poses and movements connected together by rhythm and music. Beauty and inner joy of dance is the only meaning of Nritta. It does not have any particular mood or sentiment. It produces aesthetic pleasure.
In answer to question asked by the sages, Bharata explained: "The dance is occasioned by no specific needs. It has come into use because it creates beauty."
Jathiswarams brings out three aspects of dance: unity of music, rhythm and movements. Ragam and thalam are the major aspects of Jathiswaram.
Raga can be understood as special musical space where certain patterns of swaras or tunes live in. Raga has it own mood. It guides flow of melody as cannel guides the river.
Thalam and kalam (tempo) give feeling of time. They make melody move on, define how fast it should flow.
Besides general thalam and kalam of music composition, which are constant, each dance adavu has its own rhythmic pattern. Sequences of adavus are fitting inside avartanam as sketches are fitting pages of drawing album.
Jathiswaram reminds me mountain river: streams of melodies appear here and there divided by stones of rhythmic patterns spread all along the main cannel of Ragam, bending gently to and fro, following shape of the mountain.
Message of Jathiswaram is beauty. It is pure Nritta item, thus anga shuddha (proper postures and movements) in combination with flow of melody and rhythm should evoke sense of harmony and joy of dance in hearts of spectators.
Jathiswaram includes one Jathi (adavus set to sollukattu, without any music) and several Korvays set to swaras. Jathiswaram begins with brick and fast Jathi, then two or three korvays set to Pallavi are executed. The next is one korvey set to Pallavi in combination with Anupallavi. Then follow several Korvays set to Charanas.
Jathi and Korvays are concluded with Mai adavu set to Pallavi. Mei adavu is very characteristic for Jathiswaram. It comprises mandatory body bents and rotations erformed along with steps when dancer is moveing to right and left sides at first and then backwards, or to diagonals. Mai adavu could be inserted after each Jathi and Korvay (in theory), but it would be quite monotonious to see, thus choreographers put Mai adavu after Jathi (as a rule) and them after the second of third Korvay and the last Mai adavu concludes Jathiswaram after comletion of the last korvay.
Famous Jatiswarams are composed in ragas Kalyani, Chakravakam, Arabi, Vasanta, Saveri, Kamas.
This is a song in praise of deity or some ruler. The other name of this musical composition is "Yesho geetam" (song in praise). In olden days all Shabdams were composed in Kamboji ragam. In the present day tradition, Sabdas are set to Ragamalika (garland of ragas) and Misra capu tala. The first raga is usually Kamboji, rakti raga (i.e. appealing raga providing wide scope of melodic patterns, facilitating variations of melody).
Sabdas are performed in medium or even fast tempo. Abhinaya in sabdas are always performed in a measured manner. Sancari (creative elaborations of the lyrics) are used in Sabdam in brief and moderate manner.
Shabdam starts with short jathi. Each line of sahityam is repeated several times. Dancer should explain it through pada artha (word by word) and vachika artha (sanchari) abhinaya. Each line is concluded by short jathi when the dancer executes set of simple adavus.
S Sharada Teacher adds, that Sanchari used in Shabdam should be brief .
Read more about Varnam and Swarajathi in separate section Varnam and Swarajathi.
Repertoire of devadasis comprised many Sringara Prabandhas, i.e. the songs involving one or more aspects of romantic love. Ashtapadis of Jayadeva, padam and javali genres continue this tradition on the modern stage. The padam came to music in 17th century. Many padams were composed during the period from I7th to I9th centuries by Telugu and Tamil composers.
Today Padams are considered as the most expressive element of the dance repertoire. As Jon Higgins puts it, "it is the padam which tests to the limit a dancer's interpretive range and artistic resources." 
Padam may be described as musical monologue. To understand meaning of Padam it is very essential to comprehend relationship between the heroine (Nayaki) and the hero (Nayaka). In Padam human soul is represented by female lover (Jeevatma) yearning for union with supreme being (Paramatma). This type of relationship is called "Sringara-bhakti" (devotion through love of the highest, dignified kind).
Padams give the widest scope for Abhinaya, expression of sentiments, emotions, feelings, moods including all the shades possible. Before performing a padam, the one should visualize the hero and heroine, the previous history of their relationships, the current situation, the mood and intentions of the heroine (or hero, depends upon from whose name the padam is sung) and possible development of the situation between the lovers.
Padams are suggestive and admit dual meaning and interpretation. Padams are centered round theme of love, which is basic and underlying mood of Padam. Over this mood different emotions may be expressed, according to situation and character of the heroine and hero, but they should not break the main stream of tender affectionate feeling of love flowing underneath. Anger is often pretended, suffering is mingled with hope and indignation is softened by hidden affection.
S Sharada Teacher  explains Padam as follows:
"Care should be taken when selecting the theme for a padam which is a slow item and contains a lot of deep rasa bhava. The rasa is nearly always Sringara. An idea already presented in a sanchari should not be repeated. The best charanas should be selected. The mood of the nayika should be correctly ascertained and portrayed."
Jon Higgins in his research "The Tamil Padam"  describes the nature of this relationship as follows:
"In a padam, the relationship between the nayaki, a female devotee, and the nayaka, a male deity (or human patron), is cast primarily in the mold of lover/beloved, using a tripartite rhetorical scheme in which direct communication (often confrontation) is usually mediated through a female sakhi, friend (in some Vaishnava theological interpretations, the guru), who carries messages between the two lovers, sometimes straying into the nayaka's arms along the way. This rhetorical scheme involving an indirect communication between lover and beloved. The overwhelming majority of songs in the padam genre focus on either Krishna as the nayaka (if in the Telugu language) or Murugan (if in Tamil), gods whose mythologies are saturated with youthful, playful, and virile resonances and stories."
Padams are mostly composed in Telugu and Tamil, but there are also Sanskrit, Kannada and Malayalam padams.
Sahityam of the padam should be understood on three levels:
Dr.Nirmala Sundararajan describes the theme of Padam in her lecture  as follows:
"The mood of a particular context in a padam is usually complex and is the resultant of various circumstances and problems of emotional nature. The sahitya of the padam alone may not be able to reveal the mood of the situation. When suitable music is used, the meaning of the sahitya is forcefully expressed. Most padam compositions deal with the theme of separation in love with ample scope for varied treatment and the ragams have been so shaped as to suit the theme and the context."
Thus, in Padam, the music (Raga bhava) is a powerful vehicle of simple and short sahitya. Truly, this perfect tandem of music (sangita) and words (sahitya) reflects the utmost nature of intimate deep love relationship, "words are void when the eyes are speaking." Overwhelmed with tsunami of feelings, the heroine expresses herself in a few simple and true words, energized by her emotion. Deepness, intensity and all fine shades of those emotions could be expressed only in music.
"The padams lend immense scope to expression of variegated sentiments and shades of emotion in a very leisurely tempo with exquisite raga bhava. A detailed picturization of a ragam is made possible by the use of subtle nuances and variations figuring in the music of the padams." 
Sancaras of the Raga are used very elaborately in Padam. Sancaras bring forward very important aspect of Raga called "Raga Swarupa", i.e. the most beautiful melodical phrases of the raga, which construct identity and unfold unique "character" of the raga.
Gamakas are extremely important aspect of Padam rendering. Sahityam of Padam is usually not very elaborated, just a few lines. The words of poetry (be more precise, the syllables) are prorogated, to adjust to long melodic patterns (svara phrases) of the raga. Thus, there are many Karvai (pauses, prolongations) present in sahityam of padams. Those karvais give scope for rendering gamakas, i.e. special "movements" of the notes (svaras). As melodic phrases outline Raga Swarupa, the same way Gamakas depict "shape" and "life in motion" of particular swaras.
Traditionally, Sangati (melodic variation of particular line of sahityam, showing different kinds of movements of the theme) are not widely used in Padams.
Padams are set to Rakti ragas such as Ananda Bhairavi, Shankarabaranam, Todi.
The famous composers of Padams are Kshetrayya, Sarangapani, Annamaya, Melattur Venkatarama Sastri, Kasturi Rajgaya, Swathi Tirunal, Iraiman Tambi. Ragas selected by Kshetragna for his Padams, are perfectly suitable to the sentiments and emotional atmosphere of sahitya. For instance, he employed Mohanam, Kalyani, Pantuvarali, Shri, Surutti and Kedaragaula ragas to convey Sambhoga Shringara (love in union).
Padam comprises three angas (sections), Pallavi, Anupallavi and several Caranams (three or more in number.) For dance not all charanas may be selected, just one or two the most beautiful lines are enough.
All Caranams have the same music. There are padams where the melody of Caranam is the sum of that of Pallavi and Anupallavi. In some padams, melody of Anupallavi is repeated with further development in Caranam
There is also the tradition of commencing padams with Anupallavi. The Pallavi is sung only after that followed by Caranam. The reason of such swop is, that melody of Anupallavi is relatively brighter and richer in Padams, comprising more svaras of the upper tetrachord (pa, da, ni, SA) and the Tara sthayi (upper octave). Thus, it could be said (in general) that of the three angas, Anupallavi is the best developed melody passage, followed by the Caranam and then Pallavi.
Telugu padams are always sung in a slow tempo (vilamba kalam). Tamil padams are always sung in a slightly faster tempo (vilamba or madhyama kalam). Music of Padam is slow, dignified and flows in a natural manner.
Most of the padams are set in Misra Capu and Triputa talams which help to bring out the musical gait inherent in padams.
In contrast to Padams (songs of dignified love), Javalis are songs reflecting very casual aspects of love, in light and playful manner. They emphasize amorous (and even erotic) nature of relationships between the lovers. Javalis are set to lighter ragas. It is usually sung in Madhyama kalam (medium tempo) or faster. Language of sahityam is very simple, even colloquial. It is also suggestive but in playful sense, without deep philosophical insinuations. S Sharada Teacher notices: "A padam conveys a serious emotion. The javali, which is usually faster, also conveys a serious message but in a lighter vein." 
"In form and structure the javali follows the padam, except for its lighter, more playful style. Wheat makes the javali unique is the very context of its performance, the relations that is proposes between dancer and audience." 
Javalis as dance form came into vogue in the court of Mysore, under Mummadi Krishnaraja Udaiyar III (1799-1868) and Chamaraja Udaiyar IX (1881-1894). Under patronage of those kings dance master Chinnaya (1802-1856) of Tanjore Quartette who was employed by the kings, composed many songs known as "javadi" or "javali"  . At the court of Travancore during the reign of Maharaja Swati Tirunal, another Tanjore brother Vadivelu (1810-1847) composed and staged javalis as well (more about comosers of Javalis in article published in Sruti, see Ref. 9.)
Javali was born as Telugu or Kannada genge, but in the end of 19th century javali became popular as Tamil devotional songs meant for dance. Javalis were regarded as some new, innovative compositions, and were included into performances along with Hindi or Urdu love songs and even some elements of Parsi theater (called as "Parsi Pattukal".).
Majority of performances by devadasis in 19th and early 20th centuries took place not at temples, but majorly at the salons of "new elite". Thus, from the courts of Tanjavur, Mysore and Travancore, performances migrated into salons of powerful and rich officers, dubashes, and other local chieftains of colonial Madras Presidency. Many prominent devadasis and nattuvanars from Tanjavur moved to Madras after annexation of Tanjavur to the British in 1856. This tradition of salon performance was also very common in Telugu speaking parts of the Madras Residency. Thus, javali bacame popular in court tradition of music and dance performances of 19th century, and by beginning of 20th century javali migrated into salons of colonial cities.
In javali Nayika-Nayaka relationships are portrayed in light and brick form, corresponding to atmosphere of social gathering and spirit of entertainment. The themes of javalis are bolder then those of padams. Javali deploy pure bhakti features (such as ninda-stuti or praise and complaint) inherited from padam along with open manifestation of amorous moods and even sexual metaphors. For instance, Godavari courtesans deployed rakti mudras, a set of hand gestures to depict lovemaking situation. They also performed nakha-sikha varnanam (description in praise of female body), when different art of female body are compared to images from nature like lotus, bamboo, etc. Javali could be compared to Thumri of North India and Lavani of Maharastra, i.e. dance genres whose primary function is to entertain.
The primary characters of Javali are the heroine (nayika), the hero (nayaka) and the heroine's confidant (sakhi). The heroine could address the hero directly or indirectly, through her sakhi.
Like padam javali comprises Pallavi (the refrain, which defines the reference point of the composition), Anuallavi (the bridge) and number of Caranas. The central theme is encapsulated in Pallavi. Anupallavi and Caranams have Pallavi as their point of reference, which is repeated as refrain after Anupallavi and Caranams. Such cyclic rendition allows to bring forward emotional, lyrical content of the composition, evoke memory, and move between past and present events. This is how we usually feel and brood over love situations in conversation with our close friends. The poetry of javali admits dual interpretation, it is suggestive, open-ended thus gives a lot of freedom for interpretation through abhinaya.
Besides of abhinaya, javali may include pure nritta portion called "muktayi" which is performed at conclusion of the last line of javali. In Godavari telugu region, this technique is called "gaptu varusa" or string of dance movements.
Famous composers of Javali are Pattanam Subramanya Iyer, Poochi Srinivasa Iyer, Iraiman Tambi.
The name of Tilana comprises three rhythmicsyllables: ti, la and na. The word "tilana" itself thus occurs in (the lyric of) many Tilanas. Important feature of this form is the presence of Jathis (rhythmic syllables, which comrise the mjor part of the comosition, opposite to usual padas or words or swaras or notes.) Ssahitya (lyrics) occurs onlyin the first half of the Caranam (see definition below). Domintion of the rhythmic syllables over sahityam (lyrics) makes this compostion attractive and brick.
According to many scholars, forerunner of present day Tilana is Kaivara Prabandha, which is a variety of the Prabhandha that existed in the medieval period. In this, the Jathis (or Solkattu) figured in the Matu (or the concluding session). The Prabandha begins and ends with the Patha. This aspect of the Prabandhas led the composers of the later period to evolve a new form called the Tilana. Tilana thus came to be composed by classical composers who lived in the 18th century. Melattur Veerabhadrayyah (1739-1763) is said to be the earliest composer of Tilanas and is hence called the "Tillana Margadarshi". He was the guru of Ramaswami Dikshitar.
The Kaivara Prabandha is thus the forerunner of the present day Tilana. Accordingly, the special feature of Tillana is the use of syllables which were used in the section of Prabandha called Patha, such as thakku, dikku, thaka thadingu, didingu etc.
Tillanas usually have three sections, Pallavi, Anupallavi and Caranam.
Pallavi and Anupallavi consist of Jathis, they are set in Vilamba kalam (slow or the first speed), sometimes solkattu in madhyama kalam (medium seed) are also included in.
Caranam has sahityam for the first half and is concluded by Jathi. Sahitya of Caranam is usually be in praise of a deity or the patron of the composer. Jathi portion of Caranam may include either only solkattus, or solkattu and swaras or only swaras (called citta swaras in this case), all set to Madhyama kalam. Some composers introduced special symmetrical patterns of swaras called Makutam into Jathis at the end of Anuallavi.
There are three types of Tillanas:
In a dance concert, Tilana is performed after purely abhinaya items, such as a padam, ashtapadi and javali.
Jathis emphasize the rhythmic aspects of music. As a major part of such compositions are made up of Pathas and Jathis, it facilitates the introduction of rhythmic variations and execution of adavus set to different rhythmic patterns.
There are Tilanas composed in obsolete Talams like Simhanandanam, Laksmisam, Ragavardhini, etc. which comprise many angas or structural elements such as different types of laghu, drutam, etc. Those Talams figure among ancient set of 108 talams. For instance, Simhanandanam talam comprises 128 beats in total, thus one Tilana set to this Talam would comprise only two avartanas! Such Tilanas are intended exclusively for demonstration purposes or learning (Abhyasa gana) and thus may be called Laksana Prabandhas. They help the students to learn intricate aspects of talam, such as kriyas (way of putting talam), mastering proper kalam and layam (speed and tempo), and etc.
In a music concert, Tilana figures after an elaborate Ragam-Tanam-Pallavi, towards the end of the concert. In these Tilanas the melodic aspect of the Raga is emphasized. Sangatis are used in this type of Tilana.
Melattur Veerabhadrayya and Tanjore Quartet composed Tilanas for dance.
Other famous composers of Tilanas are Swati Tirunal, Maha Vaidyanatha Iyer, Oothukkadu Venkatasubbaier, Ammachatram Kannuswami Pillai, Patnam Subramanya Iyer, Pallavi Seshaiyer, Mysore Sadashiva Rao, Veena Seshanna, Ramanathapuram Srinivasa Iyengar, Muthiah Bhagavathar, Papanasam Sivan, Mysore Vasudevachar, Lalgudi G. Jayaraman and M. Balamuralikrishna.
As dance composition, Tillana includes the following major parts (they could be called "angas" of Tillana):
Instead of conclusion, I want to quote immortal words of the great artist, the musician and the dancer, the queen of Abhinaya, Balasaraswati. Her outline of Bharata Natyam Margam given in her article , has inspired many generations of dancers to follow profession, to study and do research on dance and music.
"In the beginning, alarippu, which is based on rhythm alone, brings out the special charm of pure dance. The movements of alarippu relax the dancer's body and thereby her mind, loosen and coordinate her limbs and prepare for the dance. Rhythm has a rare capacity to concentrate. Alarippu is most valuable is freeing the dancer from distraction and making her single-minded. "
"The joy of pure rhythm of alarippu is followed by jatiswaram where there is the added joy of melody. Melody, without word of syllable, has a special power to unite us with our being. In Jatiswaram, melody and movement come together. "
"Then comes the sabdam. It is here that compositions with words and meaning, which enable the expression of the myriad moods of Bharata Natyam are introduced. "
"The Bharata Natyam recital is structured like a Great Temple: we enter through the gopuram (outer hall) of alarippu, cross the ardhamandapam (half-way hall) of jathiswaram, then the mandapa (great hall) of shabdam, and enter the holy precinct of the deity in the varnam. This is the place, the space, which gives the dancer expansive scope to revel in the rhythm, moods and music of the dance. The varnam is the continuum which gives ever-expanding room to the dancer to delight in her self-fulfillment, by providing the fullest scope to her own creativity as well as to the tradition of the art. "
"The padams now follow. In dancing to the padams, one experiences the containment. Cool and quiet, of entering the sanctum from its external precinct. The expanse and brilliance of the outer corridors disappear in the dark inner sanctum, and the rhythmic virtuosities of the varnam yield to the soul-stirring music and abhinaya of the padam. Dancing to the padam is akin to the juncture when the cascading lights of worship are withdrawn and the drum beats die down to the simple and solemn chanting of sacred verses in the closeness of God. "
"Then, the tillana breaks into movement like the final burning of camphor accompanied by a measure of din and bustle. In conclusion the devotee takes to his heart the god he has so far glorified outside; and the dancer completes the traditional order by dancing to a simple devotional verse. "
"At first, mere metre (in alarippu); then melody and metre (in jatiswaram; continuing with music, meaning and metre; its expansion in the centerpiece of the varnam; thereafter, music and meaning without metre (in padam); in variation of this, melody and metre; in contrast to the pure rhythmical beginning, a non-metrical song at the end (in tillana). We see a most wonderful completeness and symmetry in this art. "
"To train the dancer in this art, melody and metre join together in jatiswaram. The dancer takes leave of her subjective consciousness in the alarippu and identifies herself with the universal consciousness in the jatiswaram. Hereafter, she is ready to explore and express the infinity varied nuances of the entire gamut of emotions and feelings not in terms of her subjective self but in terms which bring out their universal essence. "
"Refined in the crucible of alarippu and jatiswaram, the dancer portrays the emotions of the musical text in the shabdam in their pristine purity. In the shabdam, emotions are withheld at the beginning, thereafter, when the dancer has clarified herself, they are released in a measured and disciplined manner. "
"It is after mastering this discipline that she dances the varnam which is a living river that holds together movement and interpretation. "
"It is after passing through his ordeal of fire that the dancer fully qualifies herself to do abhinaya for the padams. "
"Sringara we experience in Bharata Natyam is never carnal, never, never. For those who have yielded themselves to its discipline with total dedication, dance like music is the practice of the Presence, cannot be merely the body's rapture. "
"The dancer, who dissolves her identity in rhythm and music, makes her body an instrument, at least for the duration of the dance, for the experience and expression of the spirit. "
"However, the experience of the art can be total only if a variety of moods and feelings are portrayed; and, variety is the soul of art. But these feelings should be universalized into aspects of divinity and not remain the limited experience of an insignificant human being. The moos of a song may tend to get portrayed as the subjective feeling of one individual, but true art lies in universalizing this experience. "