Of Pallas Athena, guardian of the city, I begin to sing! Dread is she, and with Ares she loves deeds of war, the sack of cities and the shouting and the battle. It is she who saves the people as they go out to war and return again alive. Hail, goddess, and give us good fortune with happiness!
--Homeric Hymn #11: To Athena, ca. 7th century BCE
Athena, Sam & Steph Braithwaite, 2014 for Hero's Journey
Athena is famously the Greek goddess of wisdom, warfare, and general justice, which makes her one of the most beloved of her pantheon. Often called Athena Polias (Athena of the City), she is the patron goddess of the city of Athens (which in Greek is simply called Athina, the same as her name) and was its special protector and representative from the ancient days when it was a sovereign city-state until now, when it is the modern-day capitol of Greece.
Athena is first and foremost associated with wisdom, being the goddess of fair and wise counsel and mediation, which leads her to also be associated with justice, courtrooms, and legislation. The owl is her special symbol, representing as it does wisdom, and that association is so strong that large swaths of non-Greek western civilization instinctively use the owl as a representative of wisdom without necessarily even noticing why that is. (For those wondering, owls do represent wisdom in several cultures around the world, but they're more often associated with scary things like death and sorcery, probably because they're big-eyed creepsters who only come out at night. Sorry, owls.)
Although Athena does get a lot of press as a goddess of war as well, often appearing alongside or ruling over Nike, the goddess of justice, she is specifically goddess of tactics and strategy - in other words, the wisdom parts of war (the gross sticky parts mostly fall to her sibling, Ares, and his brood of shouty kids). She can and does sally forth into combat and slay enemies, appearing as a major figure in the Gigantomachy, the gods' war against the giants, and being called on to appear in most other famous Greek mythological wars as well, including the Iliad where she spends a lot of time keeping her fave, the reluctant Hero Odysseús, from getting killed while encouraging him to make smarter decisions than "run forward, stab guy in front".
God competition or beach volleyball with owls? You decide
Athena's got a lot of intriguing stories, ranging from her powers in war to her mediations between aggressors to her complete lack of sympathy for Dudes Doing Some Shit, but the easy place to start is with her highly symbolic birth. Zeus, as usual being the Worst Guy You Know, runs into the Okeanid Metis, one of the elder daughters of the great ocean Titanides Okeanos and Tethys, and as he usually does starts sleeping with her. (Unfortunately, while Metis is the goddess of cunning and prudent decision-making, this does not appear to have rendered her immune to a Zeus offensive.) When she became pregnant with Athena, however, he was told by his grandparents Gaia and Ouranos that the son she bore would be greater than he and eventually overthrow him and take the throne of Olympos. So... he ate her. You would think, having rescued all his siblings from his father Kronos when he ate them, he would have come up with a better solution than this, but apparently panicked child-consumption for reasons of monarchy is genetic.
But we're in Greek mythology today, which has the very important and unusual detail that all of its gods are immortal, eternal, and incapable of being killed (if you've ever wondered why the gods collectively put their parents in jail, this is why; there isn't really anything else they can do with them if they want to remain in control). So Metis doesn't die, of course, and just because she's inside of Zeus doesn't mean she can't do stuff, so she goes ahead and gives birth to Athena in there.
Hermes and Athena, Bartholomäus Spranger, ca. 1585
Unfortunately, Zeus did not budget gastric space for multiple probably pretty pissed-off goddesses, so he starts to suffer from debilitating pain and illness, eventually concentrating in his head, where the pain becomes so fierce that he begs the other gods to help figure out the problem and get it out of him. Athena really doesn't need their help, though, and explodes out of Zeus' head from the inside, appearing as a fully-grown adult with armor, spear and shield, and one presumes a lot of opinions about how her dad is running things out here.
Of course, this is more than just literal; since Zeus is considered a pretty wise god himself, and by eating Metis he has symbolically added her wisdom to his own, Athena popping out of his brain is a very obvious metaphor for her being the personification of all his wisdom (which is pretty hilarious because apparently the first decision Zeus' Wisdom ever made was to peace right the fuck out of Zeus). She is literally thought and intelligence made manifest. In some later versions of the story, Hephaistos is said to have helped her by splitting Zeus' forehead open from the outside while she burst from the inside, which further suggests that craft and technology are part of the process of wisdom, and also echoes Zeus rescuing his siblings from his own father's belly.
And lo, now Athena is here, lecturing warriors about not making bad Achilles-esque decisions in the heat of bloodlust, suggesting people try machines and laws instead, and generally improving the lives of humanity to an impressive degree.
I swear if you don't stop waving that sword around and pay attention to strategy, bro
Interestingly enough, the prophecy that led to Zeus eating Metis in the first place is never really addressed again in ancient Greek myth, leaving it open-ended for future shenanigans. Metis is still alive, and inside Zeus to boot; what's stopping her from just having another child, either parthenogenically or by using some of his physical form, and having the New and Improved King pop out of Zeus, too? As the goddess of cunning and good decision-making, what's she doing in there all this time? And if Athena could rip her way out of Zeus to live her own life whether he likes it or not, why didn't she bring her mother with her (her mother who, in Hesiod's account, literally made her divine armor while she was in there), and what's stopping Metis from doing the same on her own?
These questions have led a lot of modern-day Greek worshippers to consider the prophecy still active, meaning that at some future date Zeus will have a son with Metis who will overthrow him, the same as he overthrew his father Kronos and Kronos overthrew his father Ouranos. Others consider that the prophecy was fulfilled by Athena's birth, but as she's a daughter and not a son, this renders it null and void, which is just begging for modern-day worshipers to speculate about Athena's gender and whether or not this prophecy is really specific about it; after all, she's a virgin goddess who doesn't appear to have much interest in anything but her challenges and job, which lends itself very well to modern worshipers considering her androgynous, genderfluid, or generally unaffected by gendered concepts, especially since ancient Greek definitions of womanhood strongly depended on things like marriage and childbearing. Some worshipers consider Athena herself to be the fated future ruler of the pantheon, making her a sort of unexploded bomb in the middle of the Olympian political landscape that her father is ignoring due to thinking he's handled the situation.
(Incidentally, Metis does have a son according to Plato - the god Poros, lord of expediency and efficiency. But Plato tended to massage religions concepts to prove a philosophical point a lot, so it's anyone's guess whether he actually exists, is a corruption of a totally different Orphic figure, is involved here, is the Chosen One, or is just some hapless child of Metis' from before her worst date ever.)
It's no surprise that the goddess of wisdom, tactics, and fair play is very popular in the modern era. She appears as the mascot of universities, as the presiding statue outside of courthouses, and as the protector of women in sports and the military; her shrines and temples are large and lavish, starting with the famous Parthenon and its many imitators, and she is one of the most frequently prayed-to deities for anyone of the Greek religion who has to fight, strategize, or defend.
Pallas Athene, Franz von Stuck, 1898
In Hero's Journey, all Greek Heroes have access to Arete, their ability to focus on and be truly excellent and exemplary in specific areas, but Athena also grants additional Arete to her Heros, giving them extra skill in the areas of Knowledge and Tactics, teaching them by example what it means to be truly excellent when it comes to the wisdom she shares with humanity.
There's a lot to talk about with Athena, who is vastly popular, has many myths of her exploits, and continues to be one of the most important deities in the religion, but a single blog post can't do it. And that shouldn't surprise anyone; after all, how much can a five-minute read through an article try to encompass the goddess who is herself the very essence of the wise use of knowledge?