Odysseus was the King of Ithaca. He fought in the Trojan War on the side of the Greeks in circa 1200 BC. He was sceptical of Achilles' claim that the First Doctor was the Greek god Zeus.
He later believed the Doctor's story that he was a traveller in time and space, and set the Doctor the task of finding a way for the Greeks to defeat the Trojans. When the Doctor suggested a wooden horse, Odysseus insisted the Doctor accompany him inside the horse. Odysseus took part in the sack of Troy. (TV: The Myth Makers)