vanity in the odyssey?

Question

which books of the epic The Odyssey contain perfect examples of how Odysseus thought of himself as a glorious person? in other words, what are some examples in which vanity may be observed?

besides of course, odysseus yelling his name to the cyclops to tell his brothers that odysseus blinded him...thats a lil too obvious

Answer 1

Book Nine:
You can get a good example of vanity in Book Nine episode with the Cyclops when Odysseus had feasted on goat meat.
The Cyclops, whom the wanderers visit next, contrast most vividly with the Phaeacians. The Phaeacians once lived near the Cyclops but moved to Scheria to avoid the lawless brutes. While the Phaeacians are civilized and peace loving, the Cyclops have no laws, no councils, and no interest in civility or hospitality.
It is during this episode that Odysseus' judgment comes into question. Having feasted on goat meat on an offshore island, Odysseus and his men could move on. However, Odysseus is curious about who lives on the mainland. Taking a dozen of his best men, as well as a skin of extremely strong wine that he received from a priest of Apollo, Odysseus sets out to investigate a cavern near the mainland shore. It is the lair of Polyphemus, a Cyclops. Discovering abundant food in the cave, the men want to raid it and sail off, but Odysseus insists on staying to try the hospitality of the owner, who proves to be no charming host. was not the ultimate vanity?
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One should not confuse Odysseus’ pride in identifying himself to the Phaeacian hosts with vanity. One's name and reputation are crucial in the Homeric world. When Odysseus states that his 'fame has reached the skies', he is merely stating fact, identifying himself. Reputation is of paramount importance in this culture. But his pride in his name foreshadows Odysseus’ questionable judgment in identifying himself during the escape from Polyphemus.

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By the way, you mixed names in your example above.
As Odysseus and his men sail away from the Cyclops, Odysseus employs questionable judgment, shouting taunts at the wounded monster. Using the Greek's voice to direct his aim, Polyphemus hurls giant boulders after the ship, barely missing. Then Odysseus assures that his trials will continue by boasting to Polyphemus that it was he, Odysseus of Ithaca, not a "Nobody," who gouged out the giant's eye. In this instance, Odysseus is not simply showing pride in his good name, but foolish arrogance that allows the monster to identify him. Polyphemus then calls on his father, Poseidon, god of the sea, to avenge him. In a curse repeated by Tiresias as a prophecy and by Circe as a warning, Polyphemus asks Poseidon to see that Odysseus never makes it home. Or, if the Fates have already determined that he must, then may he arrive late, broken, and alone, finding great troubles in his household. With nothing but oceans between him and Ithaca and the god of the sea as his new enemy, Odysseus has paid a hefty price for his vanity.

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Answer 2

When his ego took over after the fall of Troy and his troops were singing songs of his battle prowess, it sort of went to his head. He began to believe he was greater than the gods. That is when they cursed him and he began his epic Odyessey. it took him ten years to get back home to his wife.