In the Greek camp, Ajax summons his slave, Thersites, and orders him to find out the nature of the proclamation that has just been posted. Thersites, a foul-mouthed ruffian, refuses to obey and instead curses his master and the Greeks with equal vigor, provoking Ajax to beat him. Achilles and Patroclus come upon them, and Thersites includes the two newcomers in his curses. They send him away, and Achilles tells Ajax the news of Hector's challenge to any brave Greek warrior. The selection of the warrior has been put to a lottery—otherwise, Achilles says as he leaves, he would have been the only possible choice, a remark that produces a sneer from Ajax.
In Troy, King Priam and his sons debate the wisdom of continuing the war, when they can end it by returning Helen to the Greeks. Hector, supported by his brother Helenus, argues eloquently that while the theft of Helen may have been a brave act, she cannot be worth the great and bloody price they are paying to keep her. When he is done speaking, his sister Cassandra, a prophetess who is considered mad, dashes in and cries that if they do not let Helen go, Troy will burn. When she is gone, Troilus dismisses her warning as ravings, and argues that they must keep Helen for the sake of their honor—and Paris supports him, declaring that his stolen woman is worth more than "the world's large spaces" (III.ii.162) and must be fought for. Hector retorts that this is why young men cannot be trusted to make moral decisions, since "the hot passion of distempered blood" (III.ii.169) overwhelms their reason, but when Troilus says that Helen is more than a woman, she is "a theme of honor and renown" (III.ii199), Hector yields and agrees to continue the war. He goes on to report the challenge that has been sent out to the Greeks, and how he hopes it will bring Achilles to the field.
Alone, Thersites sneers at the pretensions of both Ajax and Achilles. When Patroclus and Achilles appear, he calls them fools; Patroclus moves to strike him, but Achilles holds him off. They see the Greek commanders—Agamemnon, Ulysses, Nestor, and Diomedes—approaching, accompanied by Ajax, and Achilles quickly retires to his tent. When Agamemnon asks to see him Patroclus tells the general that Achilles is ill. Agamemnon grows angry, but Achilles refuses to emerge, and tells Ulysses, who goes in to see him, that he still refuses to fight the Trojans. Agamemnon suggests that Ajax go in and plead with Achilles, but Ulysses declares that doing so would be insulting to Ajax, and then he, with the other Greek commanders, praises Ajax profusely, saying that he is the best of their warriors. They agree to leave Achilles in his tent, and decide that Ajax will be their champion against Hector the next day.
These scenes mark the first appearances of Thersites in the play. With his constant cursing and abusive behavior, he is an unpleasant character to watch or read—but not necessarily an unsympathetic one. Although deformed, dirty, and vulgar, he is not meant to be seen as villainous or even bad—rather, he is a kind of lower-class scold, a moralist whose outbursts are occasioned by his disgust with the behavior of those around him. Most of his scenes are with Ajax and Achilles, both of whom certainly deserve his curses, and his cynicism toward the entire business of the war mirrors Shakespeare's own. All the characters in the play are desperately self-conscious—too aware, in a sense, of their role as "heroes," and not aware that their unpleasant behavior stains their heroic feats. But Thersites is aware, and his rhetoric exposes everyone else's pretensions.
"Agamemnon is a fool to offer to command Achilles," Thersites declares, "Achilles is a fool to be commanded by Agamemnon, Thersites is a fool to serve such a fool, and this Patroclus is a fool positive" (II.iii.64-67). These are all (save for Thersites himself) great heroes in Greek myth, but in this play they are reduced to foolishness. No fool is greater than Ajax, though (even Achilles seems to possess a kind of animal cunning). The scene in which the Greek leaders flatter Ajax is essentially an exercise in making Ajax look ridiculous, since everything he says is followed by a snide aside from either Ulysses or Nestor. "[If] all men were of my mind"—he begins, and Ulysses finishes by saying, "Wit would be out of fashion" (II.iii.217-18), a sentiment that fits the hapless Ajax perfectly.
Meanwhile, the conversation in Troy between Priam's sons offers another chance for philosophical and political debate—between Hector and Troilus, over the issue of whether a thing (or a woman, in this case) has only its intrinsic value, as Hector insists, or whether the only value is what we give to it, as Troilus contends. If the former is true, then they should give up Helen, since she clearly lacks enough intrinsic value to be worth so much death. But if she can be given value, as the symbol of their quest for glory, then she is worth fighting for. Hector argues eloquently against the war: he is the most heroic figure in this anti-heroic play, and so it makes sense that he is the least tainted by the blood-lust that afflicts everyone. But his capitulation at the end of the debate is stale and unconvincing; it feels as though Shakespeare wanted to develop Hector as the voice of reason, but was constrained by the details of the legendary Hector, and so had to make his character go along with the war. This is one of the difficulties with the play: because the story of Troy is so well known, the playwright is constrained by the audience's expectations.
I just finished reading Troilus and Cressida in my effort to read all Shakespeare by his 450th birthday. It wasn't a favorite play, and I probably could have had a very happy life without ever reading it. But in case you're interested, here's my take: