Ajax was a Achaean general who participated in the Trojan war. Most of what we know about him comes from Homer's epic Iliad and Sophocles' tragedy Ajax. He is well known for his gigantic stature, towering above most of the other Achaeans. Of course, given differences in height between today and some 3500 years ago, it's likely his size would not be so abnormal by today's standards.
Ajax supposedly killed himself over a contest he lost to Odysseus. He was consumed with jealousy and anger after Odysseus bested him in competition at Patroclus' funeral games.