To be Greek is to read Homer. The great epic poems of the Iliad and the Odyssey were known to all Greeks, these epic poems would be read for several days at the annual religious festivals. These Homeric epics had a far greater influence on the ancient Greek tongue than even the Bible and Shakespeare influence on the English language.
Many scholars posit that the Greek alphabet was derived from the Phoenician letters so the epics of Homer could be committed to writing. For centuries those Greeks who were literate were taught how to read and write Greek using the Homeric epics.
To appreciate these great epics we highly recommend that you listen to the lectures on these epics delivered by Professor Elizabeth Vandiver of the Great Courses.
You can also listen to free recordings available from https://librivox.org/
The Odyssey lends itself better to an audible recording, I found it tough to listen to recorded Iliad, perhaps I will try again now that I have read the epic poem. The ancient Greeks listened to these epics already knowing the plot in advance.