Cyclops, if anyone ever asks you how you came by your blindness, tell him your eye was put out by Odysseus, sacker of cities, the son of Laertes, who lives in Ithaca.
-- Odysseus to the Cyclops (Book Nine, p123 paragraph 3 (line 501))

Importance: Odysseus cannot resist calling out his name and address to the Cyclops he has just blinded. This is his fatal flaw showing - his pride. Because of this, the Cyclops' father, Poseidon the sea god, now knows exactly who to attack. This is why Odysseus suffers so much on his way home.

Tell me, Muse, the story of that resourceful man who was driven to wander far and wide after he had sacked the holy citadel of Troy.
-- Narrator (Book One, p3 paragraph 1 (line 1))

Importance: This is the famous first line of the Odyssey. This is spoken by the bard, asking for divine inspiration to tell the story correctly and well. The gods were important to the ancient Greeks, so much so that even a...