The main theme of the Odyssey is the return home, which the Greeks call nostos. The poem asks what it means to return: not merely to cross the sea, but to find the home again, the wife, the son, and the father, and to prove to each of them that one still is who one was. For this reason the theme of home always goes hand in hand with that of identity.
The return appears from the beginning: Odysseus "wandered far" after sacking Troy, and the gods decide, in the first book, that the year of his homecoming has come. Calypso and Circe want to keep him as a husband, and neither persuades him. Among the Lotus-Eaters, the fruit of the lotus makes whoever eats it forget the return. When at last he sets foot on Ithaca, the return is still not over, because the house is occupied and his wife does not recognize him. Each obstacle is a question about what a home is: the place, the people, or the name one carries.
Identity is the second axis. Odysseus loses everything, hides his name before Polyphemus, is an anonymous castaway among the Phaeacians, a beggar in Ithaca. Alcinous tells him that "no one among men is wholly without a name," and Telemachus, in the first book, says that no one knows his own origin by himself. Truth and lies enter here: Odysseus lies a great deal, always with tales "like the truth," and Athena, who knows him, laughs and declares herself his equal in cunning.
The other themes the poem develops arise from these two: the family (Telemachus, Penelope, Laertes, and the contrast with the house of Agamemnon, where the return ended in death), loyalty and betrayal (Eumaeus, Eurycleia, and Philoetius on one side, the twelve maidservants and the goatherd Melanthius on the other), and revenge, which Odysseus carries out against the suitors and which the poem closes with an imposed peace. Read this way, the poem is not merely an adventure of travel, but a reflection on what remains of a man when his place and his name are taken from him.