There’s a lot of it
The Greeks wrote a great deal, and a surprising amount of what they wrote is still available to us today, 2500 years later.
We traditionally divide Greek literature into types:
1) the epic (EH-pick):
Around 700 BC, soon after the alphabet came to Greece, Homer wrote two connected epics, the Iliad and the Odyssey. Epics are long poems which tell the story of a hero. Greek poets wrote other epics, but the Iliad and the Odyssey are the main ones that we still have complete.
2) the poem:
Two early Greek examples are Hesiod‘s Theogony and Works and Days, both from around 700 BC. There are also a number of shorter poems by Archilochus (Are-KILL-oh-cuss) and Sappho (SA-foe) from the 600s BC, among others. Sappho’s poems are unusual in being written by a Greek woman – but there are other Greek women writers too.
3) the play:
The Greeks wrote plays in verse, like poems. The plays we have are mostly the ones kids read in school (because there were more copies of them, so they were more likely to get preserved), so they’re generally about serious themes, and appropriate for school – they don’t have any sexy parts. Probably Greek theater also had lots of funny, R-rated plays too, but they’re lost now.
4) the history:
Two major histories that we still have are those by Herodotus and Thucydides. About 450 BC, Herodotus wrote a history of the Persian Wars. About 400 BC, Thucydides wrote a history of the Peloponnesian War. After the Peloponnesian War, Xenophon wrote about his adventures as a mercenary soldier for the Persians. During the Roman takeover of Greece,Polybius wrote a History of Rome in Greek. Greeks wrote history in prose (not in verse).
5) philosophical dialogues and treatises:
The first written philosophy was written by Plato around 380 BC in the form of a kind of play, two or more people talking to each other. Later on both Plato and his student Aristotle wrote regular philosophical books, in prose without dialogues.
6) legal speeches and political speeches:
History of Greek Literature, by Albin Lesky (reprinted 1996).
Greek Theatre, by Stewart Ross (1999). Easy reading.
Greek and Roman Theater, by Don Nardo. For teenagers.