From her origin as an Aegean palace goddess, Athena was closely associated with the city. She was known as Polias and Poliouchos (both derived from polis, meaning "city-state"), and her temples were usually located atop the fortified Acropolis in the central part of the city. The Parthenon on the Athenian Acropolis is dedicated to her, along with numerous other temples and monuments. As the patron of craft and weaving, Athena was known as Ergane. She was also a warrior goddess, and was believed to lead soldiers into battle as Athena Promachos. Her main festival in Athens was the Panathenaia, which was celebrated during the month of Hekatombaion in midsummer and was the most important festival on the Athenian calendar.
In Greek mythology, Athena was believed to have been born from the head of her father Zeus. In the founding myth of Athens, Athena bested Poseidon in a competition over patronage of the city by creating the first olive tree. She was known as Athena Parthenos ("Athena the Virgin"), but, in one archaic Attic myth, the god Hephaestus tried and failed to rape her, resulting in Gaia giving birth to Erichthonius, an important Athenian founding hero. Athena was the patron goddess of heroic endeavor; she was believed to have also aided the heroes Perseus, Heracles, Bellerophon, and Jason. Along with Aphrodite and Hera, Athena was one of the three goddesses whose feud resulted in the beginning of the Trojan War. She plays an active role in the Iliad, in which she assists the Achaeans and, in the Odyssey, she is the divine counselor to Odysseus.
In the later writings of the Roman poet Ovid, Athena was said to have competed against the mortal Arachne in a weaving competition, afterwards transforming Arachne into the first spider; Ovid also describes how she transformed Medusa into a Gorgon after witnessing her being raped by Poseidon in her temple. Since the Renaissance, Athena has become an international symbol of wisdom, the arts, and classical learning. Western artists and allegorists have often used Athena as a symbol of freedom and democracy.
Athena is associated with the city of Athens. The name of the city in ancient Greek is Ἀθῆναι (Athenai), a plural toponym, designating the place where—according to myth—she presided over the Athenai, a sisterhood devoted to her worship. In ancient times, scholars argued whether Athena was named after Athens or Athens after Athena. Now scholars generally agree that the goddess takes her name from the city; the ending -ene is common in names of locations, but rare for personal names. Testimonies from different cities in ancient Greece attest that similar city goddesses were worshipped in other cities and, like Athena, took their names from the cities where they were worshipped. For example, in Mycenae there was a goddess called Mykene, whose sisterhood was known as Mykenai, whereas at Thebes an analogous deity was called Thebe, and the city was known under the plural form Thebai (or Thebes, in English, where the ‘s’ is the plural formation). The name Athenai is likely of Pre-Greek origin because it contains the presumably Pre-Greek morpheme *-ān-.
In his dialogue Cratylus, the Greek philosopher Plato (428–347 BC) gives some rather imaginative etymologies of Athena's name, based on the theories of the ancient Athenians and his own etymological speculations:
That is a graver matter, and there, my friend, the modern interpreters of Homer may, I think, assist in explaining the view of the ancients. For most of these in their explanations of the poet, assert that he meant by Athena "mind" and "intelligence" , and the maker of names appears to have had a singular notion about her; and indeed calls her by a still higher title, "divine intelligence" , as though he would say: This is she who has the mind of God better than others. Nor shall we be far wrong in supposing that the author of it wished to identify this Goddess with moral intelligence , and therefore gave her the name Etheonoe; which, however, either he or his successors have altered into what they thought a nicer form, and called her Athena.
Thus, Plato believed that Athena's name was derived from Greek Ἀθεονόα, Atheonóa—which the later Greeks rationalised as from the deity's (θεός, theós) mind (νοῦς, noũs). The second-century AD orator Aelius Aristides attempted to derive natural symbols from the etymological roots of Athena's names to be aether, air, earth, and moon.