In the Iliad, Ajax is second only to Achilles of the Greek heroes. He is massive in stature; staunch in defending his fellows. He also has good sense. The Odyssey mentions a contest between Ajax and Odysseus for the arms of Achilles, who was killed by an arrow wound in the heel. (The death of Achilles is not narrated in the Iliad. Achilles is still alive at the end of this epic.)
The contest was for recognition as the warrior who had most injured the Trojans after Achilles. Trojan prisoners were the judges. Ajax committed suicide when the arms were awarded to Odysseus.
The whole story was told in a lost epic, the Aethiopis. It is not certain whether the madness of Ajax was part of the story in the Aethiopis. In another lost epic, the Little Iliad, are found the madness and also Agamemnonís decision that Ajax should not receive the customary form of burial, i.e., two of the main elements of Sophoclesí play.
The events narrated in these two lost epics (and also
in other lost epics) fall between the time of the Iliad and the
time of the Odyssey.