Ultimately, it is Apollo, the Greek god of the sun, who kicks things off between Achilles and Agamemnon. As part of his share of the Trojan war booty, Agamemnon grabs a beautiful young woman by the name of Chryseis to be his concubine, or mistress. Unfortunately for Agamemnon—but fortunately for Chryseis—the young lady's father is a priest of Apollo. As we might expect, he's not very happy at having his daughter taken from him like this. He offers to pay the Achaeans a generous ransom if they'll return Chryseis, but Agamemnon stubbornly refuses to play ball.
Apollo avenges this insult to one of his loyal servants by sending down a terrible plague upon the Achaean camp. Eventually, Agamemnon has no choice but to appease the wrath of Apollo and return Chryseis to her father. By way of compensation he takes Achilles' concubine Briseis. Achilles is absolutely furious at what he perceives as this insult to his honor, and angrily storms off to his tent. There he sulks for what seems like an eternity until he finally returns to battle after his bosom buddy Patroclus is slain by Hector.