When Odysseus first met the Cyclops, he was the epitome of an epic hero. He politely followed the Laws of Hospitality (i.e. brought wine as an offering), and answers the questions of his host. However, being an epic hero, Odysseus is clever, so rather than giving his actual name when the Cyclops asked for it, he told him his name was Nobody: "My name is Nobody: mother, father and friends, everyone calls me Nobody," (Book IX, lines 398-99). This ingenious plan worked out for Odysseus later in his visit with the Cyclops.
After watching in terror as the Cyclops dashed his men's bodies to the ground, dismembered, then ate them, Odysseus began to formulate a plan. Because he's an epic hero, he thought things through and didn't act in haste. He knew he could not kill the giant, because that would leave him and his men stranded inside the cave; none of them were strong enough to move the boulder that covered the opening. Instead, he decided to compromise the Cyclops's judgment by offering him wine. The wine was effective: "Even as he spoke, he reeled and tumbled backward, his great head lolling to one side: and sleep took him like any creature. Drunk, hiccupping, he dribbled streams of liquor and bits of men," (Book IX, lines 402-405).
Once the Cyclops was fast asleep, Odysseus and his men were free to carry out Odysseus's brilliant plan of blinding the giant cannibal by driving a smoking-hot spike into his eye. When his family members came around to see what was wrong with Polyphemus, the Cyclops, Odysseus's earlier decision to withhold his name paid off. In response to their questions of "who's tricked you, ruined you?", Polyphemus replied: "Nobody, Nobody's tricked me, Nobody's ruined me," (Book IX, line 444), freeing Odysseus from any blame.
Odysseus's epic-hero qualities of being clever, brave, and a leader are all evident in this part of the book. However, as an epic hero, Odysseus is also effected by hubris. As a result of his over-inflated sense of pride, he almost got himself and his men killed by the Cyclops in the end, and opened himself up to the wrath of Poseidon.
As they were sailing away from the Cyclops's land, Odysseus became boastful about his escape and began taunting Polyphemus from the ship: "O Cyclops! Would you feast on my companions? Puny, am I, in a Caveman's hands? How do you like the beating that we gave you, you damned cannibal? Eater of guests under your roof! Zeus and the gods have paid you!" (Book IX, lines 519-523). Of course, these words infuriated Polyphemus.
The Cyclops began ripping hilltops with his hands and hurling them at Odysseus's voice. Even though the tidal waves he created by doing so almost brought the ship back to the shore and the angry Cyclops, Odysseus continued to insult him, and eventually went too far by offering up his actual name, "Cyclops, if ever mortal man inquire how you were put to shame and blinded, tell him, Odysseus, raider of cities, took your eye: Laertes's son, whose home's on Ithaca!" (Book IX, lines 548-552).
By letting his hubris get the better of him, Odysseus informed the Cyclops of his identity and made it possible for Polyphemus's father, Poseidon, to seek revenge. As a result of his hubris, the rest of Odysseus's journey home was difficult, if not unbearable to any ordinary man.