Lord VISHNU has many avataras we cant count but we know only some avataras
matsya, kurma,varaha,narasimha,vamana,parashu rama,rama,krishna,buddha and kalki. In every soul god will present. So we cant count the avataras.

Matsya
Koorma
Narsimha
Vaamna
Parsurama
Rama
Krishna
Kalki ..yet to come ..Balrama is also considered as his avtaar and some believe Budha was also one of his avtaar .In another stream of belief his avtaars are said to be 22 .But thse ten avtaars are mostl agreed by the mainstream .

Dashavathar that means total 10 avathars.
1. malsya 2.koorma 3.varaha 4.narasimha 5.vamana 6.parasurama 7.srirama 8.balarama 9.srikrishna 10.kalki

There are considered 24 avtars out of which 23 have been taken place and 24th Kalki Avtar will be taken place about 800 yrs before end of Kalyug at Sambhal Dist.of Moradabad at Sri Vishnu Datta Sharma!s house.others are MATSAYA,KACHAP.NARAD,HANSA,HAYAGREEVA,RAM,PARUSHRAM.KRISHNA,BALRA M,BUDHDEV.VYASJI,MOHNI,DHANVANTARI,PRATHU,NARSINGH,VAMAN,SANAD,KU MARS ,RISHABDEV,NAR NARAIN

Pooja jee

All the Avatars are mortal form of Lord Vishnu, who himself is eternal, consistent and undeniable. The Dasha Avatar of Vishnu.....

Matsya Avatar - Lord Vishnu in the form of Fish
The first avatar, Matsya, was taken by Lord Vishnu at the end of the Satyuga (last age), when a flood destroyed the world. Through this avatar, he saved humanity and the sacred Veda text from the flood.

Kurma Avatar - Lord Vishnu in the form of Turtle
The second avatar, Kurma, was taken in the Satyuga (last age) to help the Devas and to obtain the amrut (nectar) of immortality which was also sought after by the Asuras (demons). He helped in creating the world by giving support of his back through this avatar.
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Oh lord when are taking the next!! we are desperate!!

Let me add to what others have written.
Haygreev, Hans

Matsaya,narsinmha. rama

MATSYA, KURMA, VAMANA, Parusurama, Rama, Krishna, NirusimhaH,VARAHA,& Kalki.