I was wondering what to do for the next fortnightly book, but some friends sent me Daniel Mendelsohn's translation of The Odyssey for Christmas, so that seems a good candidate.
Of Homer we know very little beyond the two masterpieces bequeathed to civilization in his name; modern scholars tend toward thinking that The Iliad and The Odyssey have different authors, but modern scholars have been very wrong in their assessments about these works before, so we should perhaps take that as a possibility not yet proven. The Greeks did not have a stable theology or mythology, so the occasional theological and mythological differences between the two tell us nothing (imagine trying to get a completely coherent account of the gods from Aeschylus or Plato); differences in style and vocabulary can be explained by the differences in story and theme combined with the likely differences in redaction history. If we take the two to go back, in some way, to a single poet, which we follow tradition in calling 'Homer', there is no consistent tradition about him. Some ancient stories held that he was an eyewitness of the Trojan War, others that he lived centuries afterward. The best guess, taking into account both tradition and scholarly hypothesis, is that he would have lived somewhere in the eighth century BC.
The content of the two works, on the other hand, discusses events in the Late Bronze Age, about five hundred years earlier, and allowing for distortions of time and editing, apparently well. The Iliad, in particular, has tended to trounce its scholarly skeptics; over and over again, aspects of its story that were considered purely invented have turned out to be probably about right, with some approximation. The same is true of The Odyssey, which probably does capture, filtered through some later Greek ideas and perhaps revision for narrative unity, actual Mediterranean cultures and stories from the Late Bronze Age. These cultures are often called 'palace-cultures' because they tended to be built around the palace of a war-chief who extended his protection to the community around it. Palace-culture collapsed almost completely in the early twelfth century BC; that it seems to be reflected in the interactions between kings and between kings and commoners in The Odyssey seems a sign of the latter's broad accuracy in cultural depiction.
But, of course, it is the story, not the sociology, of The Odyssey that fundamentally matters. And with that there is perhaps no better place to start off than Aristotle's famous comment, which makes it a story fundamentally about absence from and return to home:
A certain man is absent from home for many years; he is jealously watched by Poseidon, and left desolate. Meanwhile his home is in a wretched plight -- suitors are wasting his substance and plotting against his son. At length, tempest-tost, he himself arrives; he makes certain persons acquainted with him; he attacks the suitors with his own hand, and is himself preserved while he destroys them. This is the essence of the plot; the rest is episode.