Pegasus derives his name from Πηγη, or "source" because he was born at the springs of the Ocean, namely the extreme West, where Perseus killed the Gorgon Medusa. According to other versions of the myth, he was born directly from Medusa's neck, or from the Earth, fertilized by the blood of the monster. He appears in many legends: Perseus rode him when he went to free Andromeda from the rock on which she was offered as a sacrifice to a sea monster. Pegasus was later found by Bellerophon, the national hero of Corinth, who tamed him and made use of him in many of his deeds.
Bellerophon was a son of Poseidon's and of a daughter of the king of Megara, whose name varies in the different versions of the myth. Having accidentally killed a man, he had to leave his city and, in expiation of his crime, reach as a suppliant Proetus, king in Tiryns, who had the power to cleanse him of his crime. But Proetus' wife fell in love with him and, having been rejected, told her husband that he had attempted to violate her. Proetus could not take revenge personally, because it was not allowed to kill one's guests, so he sent Bellerophon to his father-in-law Iobates with a message in which Iobates was asked to kill the bearer of the missive.
On reading the letter, Iobates tasked Bellerophon with a mission that he deemed impossible: to kill the fire-breathing Chimera, a monster with the body of a goat, the head of a lion and the tail like a serpent. But Bellerophon mounted his winged horse Pegasus, flew head-on towards the Chimera with his spear and killed it in one blow. Iobates then gave him a number of further daunting quests from which the hero was victorious. Iobates then relented, believed in the innocence of the hero and gave him his younger daughter in marriage. But Bellerophon felt that because of his many deeds, he deserved to fly to Mount Olympus, the realm of the gods. His sin of presumption angered Zeus, who sent a gad-fly to sting the horse causing Bellerophon to fall all the way back to Earth.
Pegasus, instead, reached Olympus where Zeus used him as a pack-horse for his thunderbolts, and then placed him in the sky as a constellation.
The most conspicuous asterism of the constellation is the great square of Pegasus, whose vertices are the three main stars of Pegasus and the brightest star in the adjacent constellation of Andromeda.
In the Hellenistic and Roman tradition the myth is different and based the descent of Pegasus to Mount Helicon sacred to the Muses. Here he finds the daughters of the king of Macedonia, intent on a singing contest with the Muses. To their sweet melodies the springs and the rivers come to a halt and the mountain begins to grow and rise toward the sky. Poseidon then orders Pegasus to beat the ground with his hoof, and the animal does so with such energy that the growth of the mountain stops. From the hole he has opened in the ground flows the "Horse Spring", or Hippocrene, a source of poetic inspiration for those who drink its water.