Athena's epithets

Aethyia signifies a diver, and figuratively, a ship, so the name must reference Athena teaching the art of shipbuilding or navigation.

Another possible meaning may be triple-bornor third-born, which may refer to a triad or to her status as the third daughter of Zeus or the fact she was born from Metis, Zeus, and herself.

Aphaea when She was equated to a local goddess of the island of Aegina, located near Athens, once Aegina was under Athenian's power. 

Areia. Title She won for her role as judge at Orestes' trial on the murder of his mother, Clytemnestra (which he won).

Atrytone  ("the unwearying")

Cydonia the way She was known in a temple at Phrixa in Elis, which was reportedly built by Clymenus

Ergane as the patron of craftsmen and artisans. 

Glaukopis (bright-eyed orwith gleaming eyes). It is interesting to note that glaux is "little owl" (presumably because of the bird's own distinctive eyes.)

Hippeia ("of the horses", "equestrian"), as the inventor of the chariot.

Hygieia ("healer", health personified).

Parthénos ("virgin")

Parthenos ("virgin") she was especially worshipped in the festivals of the Panathenaea and Pamboeotia where both militaristic and athletic displays took place.

Polias ("of the city"), Athena was the protector of not only Athens but also of many other cities, including Argos, Sparta, Gortyn, Lindos, and Larisa.

Promachos (the First Fighter, i.e. she who fights in front).

The most accepted theory is that She was born near a lake or river called Triton.

The various Athena subgroups, or cults, all branching from the central goddess herself often proctored various initiation rites of Grecian youth, for example, the passage into citizenship by young men and for women the elevation to the status of citizen wife. 

Tritogeneia. The meaning of this term is unclear; it could mean various things, including "Triton-born", perhaps indicating that the sea-deity was her parent according to some early myths.In Ovid's Metamorphoses Athena is occasionally referred to as "Tritonia". The most accepted theory is that She was born near a lake or river called Triton.