Home, wandering, and fidelity
The title of The Odyssey has given us a word to describe a journey of epic proportions. Throughout his travels, Odysseus' central emotion is loneliness. We first encounter him as he pines away for home, alone on Calypso's beach, and he is not above weeping when thinking of home at other points. He also endures great loss through the deaths of his brothers-in-arms from the Trojan War and his shipmates afterward. Loneliness pervades the emotions of other characters; Penelope is nearly in constant tears over her absent husband, Telemachus has never known his legendary father, and Odysseus' mother explains that loneliness caused her death.
Yet tempering Odysseus' desire to return home is the temptation to enjoy the luxurious surroundings in which he sometimes finds himself -- particularly when he is in the company of beautiful goddesses. He happily spends a year on Circe’s island as her lover and does not seem to complain too much about his eight years of imprisonment on Calypso’s island. In both cases, Odysseus expresses little remorse about being unfaithful to his wife -- although infidelity is what he fears Penelope may be succumbing to at home.
That Homer never reproaches Odysseus for his extracurricular romances but condemns the unfaithful women in the poem recalls Calypso’s angry statement about the double standard for immortals: male gods are allowed to take mortal lovers, while female goddesses are not. Likewise, men such as Odysseus have some freedom to "wander" sexually during their geographical wanderings -- so long as they are ultimately faithful to their home -- while Penelope and the other women in The Odyssey are chastised for their lack of chastity. Indeed, Odysseus does remain true to Penelope in his heart, and his desire to reunite with her drives his faithful journey. Fidelity is also central at the end of the poem, when Odysseus tests the loyalties of his servants and punishes those who have betrayed him.
Cunning and disguise
Odysseus' most prominent characteristic is his cunning; Homer's Greek audience generally admired the trait but occasionally disdained it for its dishonest connotations. Odysseus' skill at improvising false stories or devising plans is nearly incomparable in Western literature. His Trojan horse scheme (recounted here) and his multiple tricks against Polyphemus are shining examples of his ingenuity, especially when getting out of jams.
Both examples indirectly relate to another dominant motif in The Odyssey: disguise. (The soldiers "disguise" themselves in the body of the Trojan horse, while Odysseus and his men "disguise" themselves as rams to escape from Polyphemus.) Odysseus spends the last third of the poem disguised as a beggar, both to escape from harm until he can overthrow the suitors, as well as to test others for loyalty. In addition, Athena appears frequently throughout the poem, often as the character Mentor, to provide aid to Odysseus or Telemachus.
Women as predatory
It is little wonder Odysseus fears Penelope's lapse into infidelity: women are usually depicted, if anything, as sexual aggressors in The Odyssey. Circe exemplifies this characteristic among the goddesses, turning the foolish men she so easily seduces into the pigs she believes them to be, while Calypso imprisons Odysseus as her virtual sex-slave. The Sirens, too, try to destroy passing sailors with their beautiful voices. The suitors even accuse Penelope of teasing them, a debatable point. But no woman receives as negative a portrait as Agamemnon's wife Kyltaimnestra; the story of her cuckoldry and murder of her husband frequently recurs as a parallel to Odysseus' anxieties about Penelope.
Odysseus' character flaws
Though he is usually a smart, decisive leader, Odysseus is prone to errors, and his deepest flaw is falling prey to temptation. His biggest mistakes come in the episode with Polyphemus as he first foolishly investigates the Cyclops' lair (and ends up getting trapped there), and then cannot resist shouting his name to Polyphemus after escaping (thus incurring Poseidon's wrath). If Odysseus' character changes over the course of The Odyssey, though, it pivots around temptation. After his errors with Polyphemus, Odysseus has his crew tie him up so he can hear -- but not follow -- the dangerously seductive song of the Sirens. Disguised as a beggar in Ithaca, he is even more active in resisting temptation, allowing the suitors to abuse him as he bides his time. Temptation hurts his crew, as well, in their encounters with Circe, the bag of winds from Aiolos, and the oxen of Helios.
The power of the gods
The gods exercise absolute power over mortal actions in The Odyssey. To curry the gods' favor, mortals are constantly making sacrifices to them. Conversely, offending the gods creates immense problems, as demonstrated by the oxen of Helios episode and Poseidon's grudge against Odysseus for blinding his son Polyphemus.
Athena is the most visible god in the poem; only under her aegis can Odysseus survive his dangerous adventures, and she lobbies Zeus for his freedom and safety at other points. Her favoritism for him seems justified as a reward for his sacrifices and nobility of character; her distaste for the suitors is similarly understandable.
The power of the gods, who usually care more about their internal disputes than about mortal behavior, is cemented at the end of the poem as Zeus orders a cease-fire between Odysseus and the suitors. Ultimately, the gods decide what happens in the mortal world; lack of free will receives more depth in The Iliad, but is a prominent theme in nearly any ancient Greek text, particularly ones that concern themselves with the omnipotent gods.
Hospitality
The Odyssey nearly serves as a Greek guide to hospitality, or "xenia," which was such a dominant concept in Greece that Zeus was the god of hospitality. Telemachus and Odysseus receive warm hospitality throughout their journeys from others, usually without even having to give their names. The flip side of the equation, of course, is the suitors, who abuse Telemachus' hospitality in running through Odysseus' reserves. The other blight on hospitality comes at the end when the Phaeacians decide not to give strangers conveyance anymore, after Poseidon turns their ship that carried Odysseus to Ithaca into stone.
Telemachus’ miniature odyssey: paralleling Odysseus' greater journey, Telemachus' journey at the beginning of the poem is as much a search for maturity as it is one for his father. Athena, who sparks his travels, also grooms him in the ways of a prince. Telemachus matures from his initial weakness in the face of the suitors into the authoritative man of the house, and his place by his father's side in the climactic battle is well earned and represented.
Revenge
Though it sweeps across many themes and aspects of human nature, The Odyssey is broadly framed as a revenge story: the climax is the slaughtering of suitors who have been vying to take over Odysseus' estate in his absence. This revenge is deeply cathartic and comes across as more well-earned because of the trials to which Odysseus was subjected at sea before he was finally "allowed" by the gods to reclaim his estate.
