One of the best reference is
srinivasaraos.blogs
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https://sreenivasaraos.com/2015/05/27/music-of-india-a-brief-outline-part-thirteen/
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For easier access, I am giving the blog post in smaller portions
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1) kirthanam
2) krithi
3) sangathi
4) ragam,tanam, pallavi
5) varnam (pada varnam, taana varnam)
6) Gitam, Svarajati and Jatisvaram
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7) padam
8) Javali
9) Tillana