Odysseus (also referred to as Ulysses in later Roman myths) is the hero in the story The Odyssey.
He was the king of Ithaca, was married to a lady by the name of Penelope, and had a son, Telemachus. He fought against the Trojans in the Trojan War. He is especially noted for his cleverness throughout Homer's poem. He was favored by the goddess Athena.
He's most famous for coming up with the idea of building the Trojan Horse and constructing that particular plan of attack. This idea came to him after ten long years of war. After the destruction of Troy, he and his men left for home without paying proper respect to Poseidon. For this, Poseidon punished Odysseus with what turned out to be a ten year journey home to Ithaca. Further insults against Poseidon complicated this journey. One insult includes the blinding of the Cyclops Polyphemus, who was the son of Poseidon. For this, Poseidon vowed Odysseus would never see his home. It wasn't until Athena petitioned Zeus for his safe return home that it actually happened.