Athena was the daughter of Zeus and Metis. But there was a problem, Zeus checked up on Metis and found out that if he had a son by her this son would be mightier than him (you know, the same way he was greater than his daddy and his daddy was greater than his grandpa). So he tricked Metis and ended up swallowing her when she turned into a fly and figured she was no longer a threat. However, Metis was pregnant with Athena and when Athena was born, this turned into quite a problem. Soon Zeus was plagued with killer headaches and he ran to Hephaestus (Smith God) and begged him to open his head. Hephaestus did as he was told, and out popped Athena, full grown and ready for battle!
Other versions peg her father as Pallas (who later attempted to ravage her and she killed him without hesitation and took his name and skin). Some say her daddy was Itonus, a King of Iton. Some say her biological father was Poseidon, but that she begged to be adopted by Zeus. No matter what the story is, she never has a real mother.
Athena's birth "is a desperate theological expedient to rid her of matriarchal conditions" says J. E. Harrison. She was the Goddess of Wisdom, and the daughter of the Titaness who basically personified it. By having her born only from Zeus, it gave males authority and power over something that had previously only been a female realm. Zeus swallowed Metis, and so was able to assimilate her crafty wisdom. Athena did not have any loyalty to a mother figure, which probably played a major role in her self-description as misogynist.
Athena was, as I said earlier, the Goddess of more things than I can shake a stick at. But they can be pretty easily summarized into three things. She was the Goddess of Wisdom, Goddess of Military Victory (war with good tactics and winning strategies, not just fighting, like Ares), and Goddess of Crafts. I need to elaborate a little more on that last one, just so you can understand her coolness. Athena invented the flute, the trumpet, the earthenware pot, the plough, the rake, the ox-yoke, the horse-bridle, the chariot, and the ship. Now that's just the "guy" stuff. She was also the first teacher of the science of numbers, and all women's arts: weaving, cooking, and spinning. If you are looking through paintings and you think you might have found something that is Athena, here is some of her iconography: the aegis (shield/fringed cloak, sometimes with the head of Medusa on it), a shield (again, sometimes with the head of Medusa), bronze armor, a helmet (this is very common), and a spear (also very common). Athena was also one of the three Virgin Goddesses on Olympus, something you might want to read more about.
I am telling this story here (briefly) because it is important to Athena (I think), but there is a much better version of this, for your reading pleasure, in the Myth Pages. So! Wayyyyyy back in the day the city of Athens belonged to Poseidon. He had claimed it by coming in, striking a rock with his trident and establishing a spring.
But the spring only gushed salt water, and so it wasn't very useful, even if it was kind of pretty. Many years later, during the reign of Cecrops (a half-snake dude who was the king there), Athena came in and planted an olive tree, thus claiming the land for herself. Poseidon was totally pissed off, and challenged Athena to mortal combat (he would have got his ass kicked) and Athena was about to accept except that Zeus stepped in and stopped them (he probably didn't want Poseidon killed). Instead they went before the Gods with Cecrops presenting the evidence. The Gods voted. All the males voted for Poseidon and all the Goddesses voted for Athena, except for Zeus - who refused to give his opinion. Therefore, Athena won the decision by one vote.
Poseidon was pissed, and - like the stupid boy he was - threw a temper tantrum and flooded another one of Athena's cities (called Athenae on the Thriasian Plain). So Athena moved to Athens, took residence there and named that city after herself too. But, to help Poseidon's ego, the women of Athens were deprived of their vote, and men were no longer to carry their mothers' names.
Athena was loved by most everyone, and was a very loving person herself. But she loved everyone in the filial sense (like a sister), and was completely uninterested in sex. There were tons of Gods who would have given their eyes to marry her, but she was completely disgusted by the idea. Once, during the Trojan War, Athena had to ask Hephaestus to make her a set of armor and weapons. She offered to pay him, but Hephaestus insisted that his only payment would be love. She completely missed the sexual innuendo and agreed. When she came to Hephaestus' smithy to pick up her stuff, he came at her and tried to ravage her. Obviously that didn't happen. Don't think to badly of Hephaestus though, it really wasn't all his fault. Poseidon had played a joke on him and told him that Athena was on her way to the smithy hoping to make violent love to him. Athena totally ran away from the unfortunate Hephaestus, but she didn't move quite fast enough and he ejaculated on her leg. Athena was completely grossed out, and wiped it off with a piece of wool that she then dropped on the Earth. That would be Gaia, and she was fertilized by the semen on the wool. Gaia was revolted at the very idea of it, and so she refused to bring the child up. Athena was fine with this and decided to bring the kid, who she named Erichthonius ("Earth-born"), up herself.
There is more to this story (involving love, suicide, and people getting turned into stone), but if you want to know it, you better check it out in the Myth Pages. Unfortunately it is not there yet, so you're just gonna have to wait.
In general, Athena was a really nice goddess. She was very modest, like Artemis, but much more generous. Athena, like Artemis, was surprised by an enraptured onlooker while bathing, but she didn't kill him or transform him or rip him to shreds or anything. She laid her hands over his eyes and blinded him, but gave him inward sight and the ability to understand the birds' signs to tell the future. As a result, Teiresias (that was his name) was highly respected and revered from then on. So that wasn't bad at all.
Athena was, as I said, generally cool. But every once in a while she got all pissy (as gods tend to get) and lashed out. Once, was a rather minor incident when she invented this double stemmed flute. She was really excited about it, and went around playing it everywhere. That is, until someone happened to mention that she looked absolutely ridiculous with her cheeks puffed out like that to play. She was furious and threw the flute onto the ground where it was picked up by Marsyas, but that's another story.
The one time Athena really lost it for something petty was in the story of Arachne, and that story isn't even really Greek. Arachne was this Lydian princess who was a fabulous weaver. She was so good that people said she was better than Athena. Athena heard and was all like, "Excuuuuuuse me? Please girl, I was weaving before humans existed," and challenged Arachne to a weave-off. They both made beautiful tapestries, and both were completely flawless, except Arachne's made fun of the Gods. Athena was bitter and very pissed and ripped Arachne's work to shreds in a cold, vengeful rage. Arachne totally didn't mean to upset her heroine and hung herself, but Athena remembered herself, and saved the girl by turning her into a spider and giving her the ability to weave forever. In a variation on the same theme, Servius reports that Athena loved this Attic chick, but the girl (Myrmex) went out and betrayed Athena's trust by claiming to have invented the plow herself, when it was really Athena. See, if they were both mortal, there would have been all this drama, someone would have gone home crying ... but Athena just turned the girl into an ant for being so presumptuous and that was the end of that.
Athena is often referred to in mythology, but if you don't know her names, sometimes these references can be hard to catch. She is often called Pallas, or Pallas Athene. This name comes from a childhood friend she had, a nymph, who she accidentally killed when they were having a mock battle. Athena was distraught and carried her friend's name with her forever more. The name, Pallas, means Maiden. And as Athena is often referred to in this form - which can refer to her Virginity, her Youthful Strength, or her Independence - you should definitely know what it means.
Often you will find references to her as "gray-eyed", a reference which seems linked only to Athena and may have something to do with her wisdom. There is one weird reference by Pausanias about Athena having blue eyes. That comes from a Libyan story that Athena was the daughter of Poseidon and Lake Tritonis, and because of that has blue eyes like her father. But this story is not generally accepted, and you aren't going to find a blue-eyed Athena anywhere except on one statue next to a specific Temple of Hephaestus, so don't worry about it. Sometimes she is called "bright-eyed" but that is common to all Gods.
In Cylarabes there is an Athena called Pania. This name, I am guessing, comes from her discovery of the flute. In Athens they called her Athena Ergane (Worker) and were very devoted to her because of her crafts. The story of her patronship of Athens is really cool, and I told it above. She was called Athena Aethyia (Gannet, a type of bird), and I don't know why yet, but there was a Rock dedicated to this where the hero Pandion died.
Tritogeneia was another name of Athena's. It could have come from three different sources. Geneia means "born" in Greek, and so it could be a reference to the idea that Athena was born from the Lake Tritonis.
It also could have been from tritô, the Aeolian word for "head", therefore "head-born" - which would make a lot of sense. The other idea is that the trito was from the root meaning "three" and that she was the third child (she was the third Olympian daughter of Zeus after Artemis and Apollo).
Okay - there are SO many epithets of Athena that I don't have room or patience to discuss all of them in detail, but here's a list I copied directly out of Robert E. Bell's Women of Classical Mythology: A Biographical Dictionary (BUY IT!): Acraea, Aethyia, Ageleia, Agoraea, Alalcomeneis, Alcimache, Alcis, Alea, Amublia, Anemotis, Apaturia, Areia, Asia, Assesia, Axiopoenos, Boulaia, Budeia, Chalinitis, Chryse, Cleidouchos, Colocasia, Coryphasia, Cydonia, Ergane, Glaucopis, Hellotia, Hippia, Hippolatis, Hygieia, Iasonia, Itonia, Laosos, Laphria, Larissaea, Lindia, Longatos, Magarsia, Munychia, Narcaea, Nedusia, Nice, Onca, Ophthalmitis, Optiletis, Oxydercis, Paeonia, Pallas, Pallenis, Panachaea, Pareia, Parthenos, Phrygia, Polias, Poliuchos, Polyboulos, Promachorma, Pronaea, Pylaitis, Saitis, Salpinx, Sciras, Soteira, Telchinia, Triton, Xenia, Zosteria.