For the sake of mankind, we are aware that the Lord manifested himself in five different forms as detailed below:
Param: Srivaikuntam considered as the 108th Divya Desam does not exist on Mother Earth.
Vyuham: Tiruparkadal considered as the 107th Divya Desam does not exist on this earth. This cannot be visited with this mortal body.
Vibhavam: To establish Dharma and wipe out the unjust, the Lord descends in various avatars as he has declared in Bhagavad-Gita.
Yada yada hi dharmasya glanir bhavati...
Paritranaya sadhoonam vinasyate...
Antarmayitvam: Paramatma resides in the innermost recess of every jivatma.
Archavataram: Manifestation in various desams, purana sthalams and temples.
Of the nine avatars the Lord has taken so far (the 10th - Kalki is yet to come), Ramavatara and Krishnavatara are considered as Poorna avatars as the Lord continued in this Bhooloka for several thousand years for the benefits of mankind even after completion of the purpose for which the descent took place.
Each avatar that has taken place and detailed in the Puranas has already been described in the Vedas. Does that mean that Vedas came into existence after the avatars had taken place? No, absolutely not. The Lord followed the Vedas in toto and only enacted what has already been stated in the Vedas.
Twenty manifestations of the Lord (apart from Kalki avatar which is yet to come), of which 10 are avatars of the Lord, are detailed in the Bhagavata Purana. His first manifestation is stated to be Kumaras (Sanaka and others) took the form of four Brahmanas and observed the hard vow of perpetual celibacy.
The various descents of the Lord are described in Bhagavata Purana known as Paramahamsa Samhita. These are detailed in the pages to come.