Parents and Siblings
Her parents are Metis (Titan of wisdom) and Zeus. Her siblings are Apollo, Artemis, Hermes, Dionysus, And Hephaestus.
Athena and Poseidon highly dislike eachother, and have been for millenia. One incident that made them hate eachother was who would patron the city Athens. The people decided it would be Poseidon or Athena, and whoever gave them the best gift would be the patron. Poseidon, being god of seas, gave them a salt-water fountain. They didn't really find it useful, so they looked to see what Athena brought. Being a wise goddess, she got them an olive tree. It was useful to the Athens, so they decided to make Athena the patron of their city, hence "Athens" is close to Athena.
Another incident has to do with Medusa. Poseidon, still angry about the Athens thing, brought a beautiful maiden, Medusa, into Athena's temple. They did things, and when Athena found out, she turned Medusa into an ugly gorgon.