Vishnu as Varaha Incarnation

Not as Vishnu's incarnation, and also in somewhat ambiguous terms, Varaha features first in the Rig-Veda, though it is in later Vedic literature that the myth begins gaining some shape. In the Taittiriya Samhita Varaha is alluded to as Prajapati's incarnation. One day, before the earth emerged, Prajapati, when as wind he roamed around in the sky, noticed the earth submerged into waters. Thereupon Prajapati transformed himself into Varaha, entered waters and lifted the earth above them. In Taittiriya Brahman it has been presented in a slightly different way. Brahma had mud deposited around the lower part of the lotus rising from his navel. Prajapati, incarnating as Varaha, collected this mud and scattered it on petals of lotus. In due course it was from this mud that the earth emerged.

However, in the Mahabharata and later in Puranas - Matsya, Linga, Vayu, Padma among others, Varaha emerges as an incarnation of Vishnu, though the myth yet related to the act of rescuing the earth. It is said that under a curse Jaya and Vijaya, door-guardians of Vishnu, were born as sons of sage Kashyapa of his wife Diti. They were named Hiranyaksha and Hiranyakashipu. Conceived in an inauspicious hour both were notorious and destructive. One day, Hiranyaksha descended the ocean and began beating its waves with his cudgel. This sent ocean into tides and tremors after which Varuna, the sea-god, rushed to Vishnu and sought his protection. Vishnu incarnated as Varaha and reached the ocean. Seeing Vishnu as Varaha heading towards him Hiranyaksha picked up the earth in one of his hands and ran to the nether world. Varaha chased him, killed him and carrying on its tusks restored the earth to its original position.