There are repeated statements in the Rig Veda which refer to the three strides with which Lord Vishnu pervades the three worlds. These refer to the Trivikrama Avatara of the Vedic period. The Taittiriya Brahmana states that God, who is the father of all, chooses His own children (the human beings) as His parents, signifying the secret of the divine descent for the good of mankind.
Incarnations of Lord Vishnu
The Satapatha Brahmana narrates the incarnation of Vishnu as a fish (Matsya). The Taittiriya Aranyaka mentions the Avatara of Lord Vishnu as a tortoise (Kurma). The Taittiriya Brahmana gives an episode of Varaha Avatara (incarnation as boar).
Types of Incarnations of Lord Vishnu
The various versions of the Avatara narrated in the Vedas are somewhat different from those found in the Indian Puranas. This variation is due to the fact that there are many numbers of Avataras that have taken place at different epochs in the continuous process of evolution and dissolution of the universe from time immemorial.
The basic theory of Avatara as found in the Vedas has been further elaborated in the Agama treatises and later in the Mahabharata and the Puranas. The philosophical and theological significance of Avatara has been fully explained in the Bhagavad Gita. This has provided the basis for the detailed formulation of the doctrine by the Vaishnava leaders.