The Odyssey opens with the gods, not with Odysseus. They are in the middle of a meeting. Poseidon is away visiting the Ethiopians at the edge of the world, and that gives Athena her chance. She argues for Odysseus, who has been trapped for seven years on an island with the nymph Calypso. Zeus agrees to let him go. But before he does, he says something worth stopping on. Mortals, he complains, blame the gods for their troubles, when they bring most of them on themselves. And he gives an example: Aegisthus, who killed Agamemnon even though the gods had sent Hermes to warn him not to. In a few lines the poem has told you its subject. The gods are involved. The people still choose.
The grievance
Poseidon is angry because Odysseus blinded his son, the Cyclops Polyphemus. And Odysseus makes it worse by his own doing. As his ship pulls away, he can't resist shouting his real name at the Cyclops, even after his crew begs him not to. It is pride, plain and simple. That boast gives the god something to aim at.
Poseidon doesn't kill him. He can't, not against the will of Zeus. What he does is delay him, and his vengeance reaches further than the hero. When the Phaeacians finally carry Odysseus home, Poseidon turns their ship to stone on the way back.
The patron
I love how odd and warm the relationship between Athena and Odysseus is. When he finally wakes up on Ithaca, she meets him disguised as a young shepherd. He doesn't know her, so he lies to her, a long, invented story about who he is. She laughs. She drops the disguise and strokes him with her hand and says that anyone who could get the better of him would have to be a crafty cheat, even if it were a god. The two of them are alike, she says, the best at schemes among men and among the gods. It is the nearest thing in Greek epic to a friendship between a god and a mortal.
The law of guests
The poem keeps coming back to one thing, the rules of hospitality. Telemachus, searching for news of his father, is fed and housed by Nestor and by Menelaus. That is how it should be done. The Cyclops does the opposite, and eats his guests. And at home on Ithaca, more than a hundred suitors have moved into Odysseus' house, slaughtered his cattle and drunk his wine while they press Penelope to marry one of them.
Zeus is the protector of strangers, and Homer's audience knew the title, Zeus Xenios. So when Odysseus comes home dressed as a beggar and one of the suitors throws a stool at him, the poem's moral sense clicks into place. The bow contest, the locked doors and the killing in Book 22 are not just revenge. They are the god of guests settling a bill. It is not an easy ending, and it gets harder when Odysseus has the maids who slept with the suitors hanged. I don't know how to defend that and I won't try. It is there, and the poem lets us feel it.
Penelope and the bed
The old nurse, Eurycleia, recognizes Odysseus by a scar, but Penelope is harder to convince. Over twenty years she has had her share of impostors. So she tests him. She tells the servants to move the marriage bed out of the room. He explodes, because the bed can't be moved. He built it himself around the trunk of an olive tree that still has its roots in the ground. Nobody but the two of them knows that. I find that more moving than any scar.
An ending people argue about
Book 24 has the relatives of the dead suitors coming for revenge, and Athena stepping in to impose peace. Some of the ancient editors in Alexandria thought the poem really ended earlier, with the reunion in Book 23. Modern scholars still argue about it. I can see why people find it a bit too neat.
There is one more piece. In the underworld the seer Tiresias tells Odysseus that after all this he must set out once more, carrying an oar, and walk inland until someone mistakes it for a winnowing fan. There he must make a sacrifice to Poseidon. Some readers think that is the real last page of the story, though the poem stops before it happens. He has to make peace with the god he angered. The poem knows that a grievance doesn't end just because the journey does.