Athena is the Greek goddess of wisdom, courage, inspiration, civilization, philosophy, justice, law, mathematics, strength, arts, crafts, skill and reason. She represents just decisions and strategic warfare and is the only goddess allowed to carry Zeus' thunderbolts. She led battles as the disciplined, strategic side of war, in contrast to her brother Ares, the patron of violence, bloodlust and slaughter.
She was depicted crowned, with a crested helm, armed with a shield and spear. She is commonly shown accompanied by her sacred animal, the owl. She is the virgin patron of Athens, which was named in honor of her (the Parthenon, which overlooks the city, was a temple the Athenians dedicated to her.) The Greeks especially also associate the olive with her, as she won a contest to decide who would be the patron god or goddess of what would become Athens when she planted an olive tree as a gift to the city.
Athena is the daughter of Zeus and the Titaness Metis. Being the father, Zeus learned that Metis' children would overthrow him like he had overthrown his father. Afraid of this, he swallowed Metis. Unknowing that Metis was pregnant, she gave birth to Athena inside Zeus, and trained her. Zeus had a splitting headache, and asked the god of forge and fire, Hephaestus, to cut open his skull. Smashing Zeus' head with his mighty ax, Hephaestus split Zeus' skull, and out sprung Athena, dressed in full battle armor.
Athena is Zeus's most powerful child. She is the patron goddess of arts and crafts, like metalworking and weaving. As goddess of wisdom, she offered wise counsel and helped promote civilization, law, order and justice. Athena inspired artists to produce the finest arts. The Athenians believed her to be resourceful and having forethought and memory. She is an extension of Zeus's role as god of humans.