Why go
The Iliad and Odyssey offer an ancient imaginative map, but Sappho, the playwrights, Byzantine authors and modern writers show different worlds. Cavafy, Kazantzakis, Seferis and Elytis are better approached as voices from their own periods than as a single unbroken classical tradition.
The full story
The Iliad and Odyssey stand near the beginning of surviving Greek literature. Their stories circulated long before modern books and remain a way into the ancient Mediterranean imagination. Classical Greece also produced lyric poetry, history, philosophical prose and drama. Sappho and Pindar wrote very different poetry; the surviving tragedies of Aeschylus, Sophocles and Euripides and the comedies of Aristophanes show the range of the stage. Greek writing continued through the Byzantine centuries in forms shaped by Christianity and the empire's intellectual life. Later, the Cretan verse romance Erotokritos, associated with Vitsentzos Kornaros, marks another world of language and storytelling. Writers of the Greek Enlightenment contributed to the ideas circulating around independence. Modern literature includes the poetry of Constantine P. Cavafy and work by Nikos Kazantzakis, George Seferis and Odysseas Elytis. Seferis and Elytis received Nobel Prizes in Literature. If a site or region makes you curious, choose a work tied to its period rather than trying to read all of Greek literature as one long preface to the ancient ruins.