Yet despite these differences, Greek religion was unified by a cast of characters - gods, heroes and men. All Greeks agree on the general outlines and stories of these characters, but the specific details vary from city to city and Greek to Greek. These divergences in details seem to serve two main purposes
The first is to lay claim to a god or hero. For example, at least six islands claimed to be the birth place of Zeus and had their own unique myths and festivals to commemorate their special relationship to the god.
Another reason Greek religion might diverge would be to explain or legitimize customs. For example, the Athenians claimed to have received their custom of trial by jury from the Goddess Athena, who held the trial of the mythical hero Orestes in Athens, ending the cycle of vengeance and bloodshed which had destroyed the Mycenaean royal family. The Athenians believed this story. The Spartans, who had no such trial system, and who held the Athenians in contempt, probably did not.
Yet, beneath these differences, the core of Greek religion remains the same. While Spartans and Athenians might disagree on how Orestes' story ends, they all agree on how it began. While half a dozen islands might claim to be the birthplace of Zeus, they all agree Zeus was nursed on an island.
Our two main sources for this universal Greek mythology are Homer and Hesiod. Aside from the Iliad and the Odyssey, the Greeks attributed several hymns to the various deities to Homer. These hymns provide brief scenes from the lives of the gods, from the birth of Hermes to Aphrodite's stormy love affair with Anchises. Beyond these, there seem to have been other, older myths floating around Greece. Around 800 BCE, the poet Hesiod attempted to wrap all of these myths into a single coherent creation story. The result is Hesiod's 'Theogony'. Between the hymns and epics of Homer and Hesiod's 'Theogony', we can construct a general outline of Greek mythology.