Odysseus is also know in Roman times as Ulysses, and is most famous for his long voyage back from the sacking of Troy, (related in the Odyssey) and the adventures he had on his way back home.

The story of his joining in the Trojan War is less than complimentary:
Visited by Agamemnon and Menalaus on their search to engage the best fighters and most heroic men for the assault against Troy. Seeking to avoid enlistment, Odysseus pretended to be insane. He had a good life with his faithful wife Penelope and his young son Telemachos, living on the island of Ithaca.
He put on a fisherman's hat, yoked a horse and an ox together, and commenced to plough. But when his son was placed in the path of the plough, Odysseus had to swerve aside, thus proving he was indeed sane, whereas he was taken to fight at Troy.

Born a son of Laertes, king of Ithaca, Odysseus was fated to distinguish himself in the coming war, and become a hero. In the Trojan War he fought well, leading the Greek forces with Achilles, and it was to him that the latter's famed armor was awarded, on Achilles death. It was also Odysseus who made the prophet Helenos, brother of Priam, disclose to the enemy the means by which the city might be taken. These were the assistance of Achilles' son, Neoptolemos, the bow and arrows of Hercules and the possession of the Palladium, an image of Pallas-Athene. The first condition was easy to fulfill, as Neoptolemos, languishing in Skyros, was eager for battle. Odysseus journeyed there to bring the boy back to Troy. The second part of the bargain, however, was a little more difficult. The bow and arrows of Hercules were in the possession of Philoktetes, who had been abandoned on the island of Lemnos by the Greeks, who had not cared to endure the screams of the injured man, after he had hurt his foot. Philoktetes was not kindly disposed towards the Greeks. But Odysseus traveled to Lemnos anyway, and succeeded in tricking Philoktetes into coming to Troy, where his wound was healed, and the grateful Philoktetes handed over the weapon. The first victim it claimed was the instigator of the war, Paris.

After his fall, the Trojans shut themselves up in their city, afraid to come out. The capture of the Palladium was a somewhat different matter. This was held within the walls of the besieged city, and again it was the brave Odysseus who ventured inside, disguised as a beggar, to find out where the idol was kept. Then returning with Diomedes he captured the statue, brought it back to the Greek camp—thus fulfilling the third and final condition for victory. Next came the celebrated strategy of Odysseus who, on the advice of Athene, had a large horse of wood constructed, and within concealed soldiers of Greece, himself included. The rest of the Greek fleet then set sail, giving the impression that they had abandoned the city.
The Trojans suspiciously asked the freed Sinon, a friend of Odysseus whom the hero had left bound on the shore, as in a sacrifice, and whom King Priam had taken pity on, what the idea of the horse was. Sinon replied that it was a sacred object, and that if the Trojans took the horse into their city, they would be under the divine protection of the gods. Delighted, the Trojans followed Sinon's advice, taking the wooden horse in through the gates of the city, and reveled and partied all night, celebrating their deliverance from enemy, until they all fell into a drunken sleep. Now Sinon approached the horse, opening a secret door in its side, and the Greeks emerged from the hollow horse, signaling to the fleet, which lay at anchor not far away. Returning silently and entering the city, the Greeks fell upon the surprised Trojans and slew most of them, putting the city to the torch and carrying off their women.

Returning from the now-conquered city, Odysseus had his most famous adventures after being blown off-course from his homeward track. The first place he came to was the country of the Cyclops, where in a cave he met one of them, Polyphemos, a son of Poseidon. Odysseus and his men had taken shelter in the cave, the Cyclops being absent at the time. As evening fell, the giant returned with his flock of sheep, and closed up the cave entrance with a huge stone.
Upon discovering the strangers, he ate two of them, and then fell asleep. When he left the following morning, taking his sheep to pasture, he again closed over the entrance to the cave. After some nights of this--and the loss of several men--Odysseus hit upon a plan for their salvation.
When the Cyclops had eaten his usual meal, the hero offered him some wine. Never having tasted the drink before, Polyphemos shouted for more, which they gave him until he fell into a drunken sleep. Then Odysseus and some of his men heated a long pole, and with it burned out the single eye of the Cyclops. Waking in a fury, blinded, Polyphemos groped around for the men, but was unable to find them in the darkness. He removed the stone at the mouth of the cave, and sat there, while his sheep ambled out. He meant to grab the humans as they ran out, but Odysseus and his men had fastened each of themselves to the belly of a sheep, and as the Cyclops counted and felt the fleece of his herd as they emerged, Odysseus and his men passed out safely. Once out and safely on the way back to the ship, Odysseus cried back jeeringly at the giant, giving his name as 'Nobody'.
Polyphemos, imploring the aid of his brothers, cried out that he had been sorely wounded, but when they asked by whom, he answered ‘Nobody’. They laughed, saying that if Nobody had hurt him, what was he howling for? Enraged and frustrated, the Cyclops called upon his father, Poseidon, to punish those who had maimed him. The sea god did just this, blowing Odysseus' ships even further off-course, until he arrived at the island of Aeolos, king of the winds.
Aeolos received him courteously, presenting him at his departure with a bag containing all of the unfavorable winds, that Odysseus not be troubled any further.
Odysseus attempted to stay awake until they reached home, but as their home port came into view, he finally slept. As the captain slept his men became curious as to the contents of the bag. Finally, they could stand it no longer and opened the sack, releasing the wild winds, which blew them far out to sea.

This time the ships of Odysseus were blown towards the island of the sorceress Circe, whose first act was to transform Odysseus' men into swine. Softened by the hero's manner, the witch relented and changed his men back, and entertained the party there for a year. After this she advised Odysseus to journey to the Underworld, there to enquire of the shade of the seer Teiresias as to the fate in store for him. Taking her advice,the Greek hero traveled to Hades, meeting many former friends of his, and returned to Circe

Next of his adventures was to be the first mortal to successfully pass the infamous Sirens, whose singing drove men mad, and caused them to land on the shores of Sicily, where the Sirens devoured them. Ordering himself bound to the mast and his men’s ears plugged, Odysseus gave strict instructions that, no matter what he said during the passage through the country of the Sirens, he was not to be released until they were safely through.
His men followed his orders, and though the hero strained at his bonds and frothed at the mouth, they would not untie him until they were safely past. Thus Odysseus became the first man to hear the song of the Sirens and live, and as a result of this the ancient enchantment of the Sirens was broken, and their power was destroyed.
The expedition successfully passed the monsters Scylla and Charybdis, and landed on the island of Trinakia, where grazed the sacred flocks of the sun god.
Despite the warnings of both Circe and Teriesias, they plundered the herd, and as a punishment were struck at sea by a terrible storm, in which all of Odysseus' men died. He, clinging to a piece of driftwood for nine days, finally washed up on the shores of the island where lived the nymph Calypso.
Odysseus pined for seven years on the shores of that island, until finally Calypso was forced by the gods to release him. Despite the entreaties of the nymph to remain with her Odysseus left the island on a handmade raft. But he was blown about again by Poseidon, and he would have perished, had it not been for the timely intervention of the sea nymph, Leukothea. Upon swimming to land, the daughter of the king of the Phaeakians found Odysseus, and after spending some time there, relating his stories to the king, the hero was sent home in a great ship.

Returning to his own land, Odysseus found that his wife had remained faithful to him through all those years, despite the many suitors who had vied, and were still vying for her hand. Together with his son Telemachos, now grown to manhood, he came among the suitors, raised a quarrel and slew them all. After putting down an insurrection masterminded by the friends of the dead suitors, Odysseus spent the rest of his life reigning peacefully over Ithaca, his travels and adventures at last at an end.