Pallas Athena (Minerva in Roman) was the Goddess of wisdom, civilization, warfare, strength, strategy, female arts, crafts, justice, heroic endeavor, philosophy, and skill. She was also a common companion of Heroes and was the patron of Athens, the city named after her. Another thing she was known for was being one of the three virgin Goddesses.
The most popular story of her birth is that Zeus (Jupiter in Roman) had an affair with Metis. Afterwards, he discovered that any children he had with Metis would be greater than himself. As a result, he swallowed Metis to prevent a pregnancy. What he didn't know was that she was already pregnant with Athena. Metis gave birth to Athena and nurtured her inside Zeus until he complained about headaches. Hephaestus (Vulcan in Roman) split open his head with his smithing tools. Athena burst from his forehead fully grown and armed with weapons.
Other tales of her birth are that she was created parthenogenically as a daughter of Metis. Another story is that she came from another pantheon and was "adopted" by the Greeks as an Olympian.
Hephaestus once attempted to rape Athena, but she escaped. His semen fell upon the earth and impregnated Gaea, creating Erichthonius. Gaea gave the baby to Athena to raise the baby as her foster mother. Once he was grown, became the founder of Athens, and its first king. Many beneficial changes to Athenian culture could be traced back to him.
Athena competed with Poseidon (Neptune in Roman) to be the patron deity of Athens, which hadn't been named yet. They agreed each would give the people of the city a gift, and whichever gift the people preferred would name the patron deity. Poseidon struck the ground with his trident and created a spring, giving them a way to trade, not to mention easy access to fresh water. Athena offered them the first domesticated olive tree. The current king of the city, Cercrops, accepted the olive tree on behalf of the people. He also named the city after their patron deity.
She created Medusa, then guided Perseus in his quest to behead the monster. She helped Heracles skin the Nemean Lion, defeat the Stymphalian Birds, and navigate the underworld. She helped Odysseus on his voyage home after the Trojan war and win his kingdom back upon arriving home. She also created the first spider, Arachne.