The Iliad and the Odyssey are epic poems composed by the Greek poet Homer. They are complex works with many interwoven plot lines, highly developed characters, and fascinating settings, so a summary of both of them will necessarily be shallow at best and focus only on the high points of the narratives.
The Iliad opens in media res, in the midst of things. The Trojan War has already been going on for over nine years, and the Greeks are not doing too well at this point. They have even been hit by a plague, and Agamemnon discovers that the Greeks' capture of two Trojan women, Chryseis and Briseis, lies behind the illness. Agamemnon holds Chryseis and decides he will give her back, but then he wants Achilles to give him Briseis instead. Achilles is so offended that he decides to sit out the rest of the war.
Things continue to go rather badly for the Greeks. Achilles still stubbornly refuses to participate, but he decides to send his friend Patroclus to fight in his place, even giving him Achilles's own armor. The Trojan Hector kills Patroclus and takes the armor. This enrages Achilles and draws him back into the fight. He kills every Trojan in sight and eventually slays Hector as well. Achilles, however, is not satisfied with Hector's death. He attaches the Trojan's body to his chariot and drags it around the city for nine days. The poem ends with a god-negotiated truce, and Achilles returns Hector's body to his father, King Priam.
The Odyssey picks up the story ten years after the Trojan War. Greek hero Odysseus has not yet made it home to Ithaca, and his wife, Penelope, is plagued by suitors who want to marry her and get control of Odysseus's estate. Penelope, supported by her son, Telemachus, has resisted for years. Odysseus is alive, just as Penelope thinks, but the nymph Calypso has been holding him captive. Telemachus, helped by the goddess Athena, makes a voyage to find out the truth of the matter.
Meanwhile, Odysseus escapes from Calypso and ends up with the Phaeacians. He tells of his fantastic exploits since leaving Tory: the Lotus Eaters, the Cyclops, Circe, the Sirens, his trip to Hades, and the monster Scylla. Odysseus then goes home to Ithaca, only to find his house filled with suitors. He identifies himself to his son but disguises himself as a beggar in his own house. Penelope holds a contest and promises to marry the suitor who can string Odysseus's bow and shoot an arrow through twelve axes. Of course, Odysseus himself is the only one who can do that. His identity is revealed, and Odysseus and Telemachus kill all the suitors.