He was described as fearless, strong and powerful but also with a very high level of combat intelligence.
Ajax commands his army wielding a huge shield made of seven cow-hides with a layer of bronze.
Ajax argues that because of his strength and the fighting he has done for the Greeks, including saving the ships from Hector, and driving him off with a massive rock, he deserves the armor.
However, Odysseus proves to be more eloquent, and with the aid of Athena, the council gives him the armor.
He is also referred to as "Telamonian Ajax" ( Ajax is the son of Telamon, who was the son of Aeacus and grandson of Zeus, and his first wife Periboea.
In Book 14, Ajax throws a giant rock at Hector which almost kills him.
In Book 15, Hector is restored to his strength by Apollo and returns to attack the ships.
Ajax at first gets the better of the encounter, wounding Hector with his spear and knocking him down with a large stone, but Hector fights on until the heralds, acting at the direction of Zeus, call a draw, with the two combatants exchanging gifts, Ajax giving Hector a purple sash and Hector giving Ajax his sharp sword.
The second fight between Ajax and Hector occurs when the latter breaks into the Mycenaean camp, and fights with the Greeks among the ships.Ajax is responsible for the death of many Trojan lords, including Phorcys.