This play by Sophocles is about the circumstances surrounding Ajax's death towards the end of the Trojan war. It has a strange structure to a modern reader. We take up the action in a conversation between Odysseus and Athena, after Odysseus is trailing the man who has killed all the Greek cattle and sheep. Athena reveals that this is Ajax, who in rage over Odysseus being awarded Achilles armor has set out to slaughter all the Greeks. However, Athena made him mad and he delusionally killed or tortured all the live stock. To cut this summary short, Ajax later comes to his senses goes off and kills himself with Hector's sword and then there is a long debate about whether the body should be buried or left to rot and be eaten by wild animals. This is the kind of plot line that only the Greeks would come up with.
In fact, I think that Ajax is a pretty good play. While definitely not amongst the best of surviving Greek plays, all surviving Greek plays are pretty good. It has a lot of stirring scenes and surprisingly an on stage suicide. It would be fascinating to see a modern staging of Ajax because it would present so many challenges. The version I read was a verse translation and the writing is good and the characterization about average for Sophocles.
The major drawback to the play is that it is so incredibly Greek. At this point, I have read so much by the ancient Greeks and so much about the ancient Greeks that I feel that I know their culture decently well. However, to someone not familiar with it, much of the play would be unfathomable. The relationship to the Goddess Athena, the factious fighting over trivial things by the Greek allies and most of all ending the whole emotionally over-wrought play in an extended discussion of the appropriate way to bury Ajax's body are difficult places to start.
In fact, the point of the play is most of all the debate about the burial. In that debate we see two very typical Greek ideas. First, we see the idea that a persons life cannot be judged until after their life, where the whole of that life is taken into consideration. Odysseus, Ajax's later enemy and the symbol hear of a cunning-wisdom argues that while, Ajax did just try to murder him, taking his life as a whole he was noble. Very Greek idea. Furthermore, by burying him a potential cycle of offending the Gods can be avoided, so we don't end up with the kind of reprisals and counter-reprisals that we see in Sophocles' Argos cycle of plays. Also a very Greek idea. The whole thing is very Greek in general, and very Sophoclean in particular, but a poor place to start for someone starting out with Greek Theatre.