Ajax is the earliest of Sophocles' s surviving plays. It is thought that the play's first performance took place about 444 B.C., but the exact date is not certain and might have been a few years earlier or later.

The hero of the play, Ajax, illustrates the uncompromising nature of the noble warrior; yet at the same time, he also represents the failings of excess pride, or hubris. Ajax believes that he deserves the armor of Achilles, and he is unable to accept that another warrior has been chosen as more worthy. His pride will not permit him to see the strength of Odysseus, nor will it allow Ajax to recognize his own limitations.

Ajax is a great hero, but he is rigidly defined as the old-fashioned hero - uncompromising and unable to recognize his own weaknesses. It is his rejection of help from the goddess Athena that sets the stage for this tragedy. Athena's gloating punishment of Ajax also presents the gods in a less favorable way than earlier plays, such as Aeschylus's Oresteia, which portrays the gods as wise protectors rather than vengeful deities.

Sophocles's source was probably Homer, who depicted Ajax as obstinate to the point of stupidity in The Iliad. Both Ajax and Odysseus fought bravery with Achilles, and it took both warriors to retrieve Achilles's body after his death. Both men were honorable, but the Greek commanders voted that Achilles' s armor should be awarded to Odysseus. This act provides the impetus for Ajax's actions, which take place just prior to the opening of Sophocles's play.