Matsya, (Sanskrit: “Fish”) is one of the 10 avatars (incarnations) of Lord Vishnu. In this appearance, Lord Vishnu saved the world from a great flood.
Manu, the first man, caught a little fish that grew to giant size. When the flood approached, Manu saved himself by tying his boat to the horn on the fish's head. Matsya is listed as the first Dashavatara.
Kurma ('Tortoise'), is an Avatar of Lord Vishnu. Originating in Vedic literature such as the Yajur Veda as being synonymous with the Saptarishi called Kasyapa, Kurma is most commonly associated with the story of the churning of the Ocean of Milk, referred to as the Samudra Manthan. Kurma is the second Dashavatara.
Varaha ("boar") is the avatar of the Lord Vishnu, in the form of a boar. Varaha is most commonly associated with the story of lifting the Earth (personified as the goddess Bhudevi) out of the cosmic ocean.
When the demon Hiranyaksha stole the earth and hid her in the primordial waters, Lord Vishnu appeared as Varaha to rescue her. Varaha killed the demon and retrieved the Earth from the ocean, lifting it on his tusks, and restoring Bhudevi to her place in the universe. Varaha is listed as third Dashavatara