Identity of Ajax: Ajax was the son of Telamon, the king of Salamis. He was one of two Trojan War heroes named Ajax who was on the side of the Greeks.

Ajax and the Achaeans: Ajax was one of the suitors of Helen, for which reason he was obliged by the Oath of Tyndareus to join the Greek forces in the Trojan War. Ajax contributed 12 ships from Salamis to the Achaean war effort.

Ajax and Hector: Ajax and Hector fought in single combat. Their fight was ended by the heralds. Hector and Ajax then exchanged gifts, with Hector receiving a belt from Ajax and giving him a sword. It was with the belt of Ajax that Achilles dragged Hector.

Suicide of Ajax: When Achilles was killed, his armor was to be awarded to the next greatest Greek hero. Ajax thought it should go to him. Ajax went mad and tried to kill his comrades when the armor was awarded to Odysseus, instead. Athena intervened by making Ajax think cattle were his former allies. When Ajax realized he had slaughtered the herd, he committed suicide as his only honorable end. Ajax used the sword Hector had given him to kill himself.

Ajax in Hades: Even in his afterlife in the Underworld Ajax was still angry and wouldn't speak with Odysseus.