In the Hindu Scriptures it is told that there will be ten avataras, of Vishnu (the so called dasavatara).

In the Srimad Bhagavatam, Canto One, Chapter Three, this list is expanded upon and 22 purusha(*) incarnations are listed:

  1. Kumaras Incarnation;
  2. Sukara (Varaha) Incarnation(**);
  3. Narada Incarnation;
  4. Nara-Narayana Incarnation;
  5. Kapila, the Author of Sankhya Philosophy;
  6. Dattatreya Incarnation;
  7. Yajña Incarnation;
  8. Rishabha Incarnation;
  9. Prithu Incarnation;
  10. Matsya Incarnation(**);
  11. Kurma Incarnation(**);
  12. Dhanvantari Incarnation;
  13. Mohini Incarnation;
  14. Nrisimha Incarnation;
  15. Vamana Incarnation;
  16. Bhrigupati (Parashurama) Incarnation(**);
  17. Vyasadeva Incarnation;
  18. Rama Incarnation(**);
  19. Balarama Incarnation;
  20. Krishna Incarnation(**);
  21. Buddha Incarnation(**); and
  22. Kalki Incarnation(**).
Dasavataras in bold.

Chapter seven of the Second Canto, recounts a number of these -- as scheduled incarnations with specific functions -- and also includes Hayagriva, and Manvantara. However, scripture itself makes clear that the incarnations of the Lord are actually inexhaustible:

"avatara hy asankhyeya
hareh sattva-nidher dvijah
yathavidasinah kulyah
sarasah syuh sahasrashah

O brahmanas, the incarnations of the Lord are innumerable, like rivulets flowing from inexhaustible sources of water."

Bhag., Canto 1, Ch. 3, Text 26

(*) The gloss my copy gives is "the expansions of Vishnu as creator of the Universe".
(**) An avatara of Vishnu.

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