Odysseus
Odysseus was a legendary, possibly actual, Greek king of Ithaca, the focal point of certain literary works, and also entering into others.
The basic story
Odysseus was king of Ithaca at the time the Trojan war was starting. The Achaeans came to seek his help. Having been warned by an oracle, Odysseus tried to evade them through a pretence of madness, ploughing with an ox and ass yoked together, while wearing a peasant's hat. However, he abandoned the pretence when his infant son Telemachus was placed in front of the plough. At the siege of Troy, Odysseus was one of the principal commanders, establishing a reputation for guile, but also for valour, to such an extent that after the death of Achilles he was awarded the arms of the dead hero, to the fury of Ajax, who thought he had a better claim on them.
After the sack of Troy, Odysseus set out on his return home, a journey which took him ten years, owing to the enmity of the god Poseidon, who hated him both as one of the victors over Troy and as having blinded his son, the Cyclops Polyphemus. The standard account is given in the epic poem, the Odyssey of Homer. There are differing accounts of Odysseus's death.
Ulysses
Odysseus was known as Ulysses to the Romans, who tended to regard him as a treacherous villain, pure and simple. He appears under this name in Virgil's Aeneid, in Dante's Divine Comedy (Canto 26 of Inferno), in Shakespeare's Troilus and Cressida, and in a poem of Tennyson. The name is also used for the title of James Joyce's novel, in which the events parallel the Odyssey. Whereas the original epic presents the hero as a home-seeking man, Dante depicted him as a searcher, seeking out new experiences, and this was the theme taken up by Tennyson. Joyce is somewhere between the two.