Her father is Zeus, and her mother Metis, a previous goddess of wisdom. When Zeus found that Metis was pregnant, he swallowed her in fear that she would bear a son who would be stronger than he. She began to make a robe and helmet for her daughter, causing Zeus agony with her hammering of the metal. Hephaestus ran to his father and split his head open with an axe in an attempt to relieve the pain. From Zeus’ open skull, Athena emerged, fully grown and wearing the clothing her mother had created. Athena became his favourite child and advisor, entrusted with the aegis and the location of his thunderbolts.
She was thought to have had neither sexual consort nor offspring. She did have a foster son, though. Hephaestus attempted to rape Athena, and was unsuccessful. His seed fell to the earth, from which Erichthonius grew. Gaia did not like the situation, and did not want the child. She put the child in a basket and gave it to Herse, Pandrosus, and Aglaulus (sisters and Athenian priestesses), demanding that they never open it. Herse and Aglaulus went against her wishes, opened the basket, went mad at the sight, and threw themselves off the Acropolis. A crow saw this and flew to tell Athena, who had gone to bring a mountain for use in the Acropolis. In a rage, she dropped the mountain, which is now called Mount Lykabettos. Athena took the child to raise and educated him well. He eventually became the King of Athens.
A woman named Arachne once inadvertently challenged Athena to a weaving contest while bragging to other women. At the end of the contest, Athena deemed Arachne as skilled as herself. Then she saw the subject of the mortal’s tapestry- the failings of the gods. She ripped the work to pieces, then touched the woman’s forehead, making her feel shame. Arachne hung herself. Athena took pity on her and sprinkled her with the juices of aconite, causing her ears, nose, and hair to fall off, her form to shrink up, and her fingers to cleave to her sides as legs; thus creating the first spider.
In another legend, Athena and Poseidon were both enamoured of a city in Greece. Both claimed the city, and it was decided that it would be given to whoever could give it finest gift. Among a crowd of the citizens, the goddess and god mounted the Acropolis. Poseidon raised his trident and struck the side of the cliff, where a spring welled up. The people marvelled at this, but the water turned out as salty as the sea, so it was not very useful. Athena stamped her foot on the ground and an olive tree sprang forth, giving the people food, oil, and wood. They awarded the city to her, and she named it Athens.
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I've edited this post to make a permanent place for requests. It's linked in the userinfo, so it'll be easier to find when needed. So, when you have a request, please direct it there from now on. :)