Achilleus and Agamemnon fight over Briseis. Achilleus gets in a huff and refuses to fight for the Achaians anymore. Instead, he gets Zeus to beat up on the Achaians so they'll know how much they miss him. After the Achaians do start getting beaten up, Agamemnon tries to put aside his differences with Achilleus, but Achilleus refuses.
Finally, when things are looking bad for the Achaians, Patroklos convinces Achilleus to let him lead the Myrmidons into battle, wearing Achilleus's armor. This succeeds in driving the Trojans away from the Achaians' ships, but then Patroklos is killed. Achilleus swears revenge, gets a new suit of armor from the gods, comes back into battle, and kills many Trojans, including Hektor.
Even after killing Hektor and burying Patroklos, however, Achilleus can't let things rest. He keeps moping around, weeping, and abusing Hektor's body until finally the gods decide to put a stop to it. They get Thetis, Achilleus's mom, to convince him to give up the body, and send King Priam to ask for it. When he arrives, he and Achilleus share a moment of common humanity. They negotiate a truce between the armies so that Hektor can be buried in peace.