Medusa

The three Gorgon sisters—Medusa, Stheno, and Euryale—were children of the ancient marine deities Phorcys and his sister Ceto, or sometimes (and much less probably), Typhon and Echidna, in each case chthonic monsters from an archaic world.

 This painting above of her head is by an unknown Flemish artist.

Their genealogy is shared with other sisters, the Graeae, as in Aeschylus's Prometheus Bound, who places both trinities of sisters far off "on Kisthene's dreadful plain":

Near them their sisters three, the Gorgons, winged
With snakes for hair— hated of mortal man—

While ancient Greek vase-painters and relief carvers imagined Medusa and her sisters as beings born of monstrous form, sculptors and vase-painters of the fifth century began to envisage her as a being both beautiful as well as terrifying. In an ode written in 490 BC Pindar already speaks of "fair-cheeked Medusa".

In a late version of the Medusa myth, related by the Roman poet Ovid (Metamorphoses 4.770), Medusa was originally a beautiful maiden, "the jealous aspiration of many suitors," priestess in Athena's temple, but when she was raped, or seduced, by the "Lord of the Sea" Poseidon in Athena's temple, the enraged virgin goddess transformed her beautiful hair to serpents and made her face so terrible to behold that the mere sight of it would turn a man to stone. In Ovid's telling, Perseus describes Medusa's punishment by Athena as just and well-deserved.

In the majority of the versions of the story, while Medusa was pregnant by Poseidon, she was beheaded by the hero Perseus, who was sent to fetch her head by King Polydectes of Seriphus as a gift.

With help from Athena and Hermes, who supplied him with winged sandals, Hades' cap of invisibility, a sword, and a mirrored shield, he accomplished his quest.

The hero slew Medusa by looking at her harmless reflection in the mirror instead of directly at her to prevent being turned into stone.
When the hero severed Medusa's head from her neck, two offspring sprang forth: the winged horse Pegasus and the giant Chrysaor who later became the hero wielding the golden sword.

This painting of the head of Madusa is by Caravaggio

Jane Ellen Harrison argues that "her potency only begins when her head is severed, and that potency resides in the head; she is in a word a mask with a body later appended... the basis of the Gorgoneion is a cultus object, a ritual mask misunderstood."

In Odyssey xi, Homer does not specifically mention the Gorgon Medusa:

"Lest for my daring Persephone the dread,
From Hades should send up an awful monster's grisly head."

Harrison's translation states "the Gorgon was made out of the terror, not the terror out of the Gorgon."

According to Ovid, in North-West Africa Perseus flew past the Titan Atlas, who stood holding the sky aloft, and transformed him into stone. In a similar manner, the corals of the Red Sea were said to have been formed of Medusa's blood spilled onto seaweed when Perseus laid down the petrifying head beside the shore during his short stay in Aethiopia where he saved and wed his future wife, the lovely princess Andromeda.

Furthermore the poisonous vipers of the Sahara, in the Argonautica 4.1515, Ovid's Metamorphoses 4.770 and Lucan's Pharsalia 9.820, were said to have grown from spilt drops of her blood.

Perseus then flew to Seriphus where his mother was about to be forced into marriage with the king. King Polydectes was turned into stone by the gaze of Medusa's head.

Then he gave the Gorgon's head to Athena, who placed it on her shield, the Aegis.h/t wiki