What are Agamemnon and Achilles most concerned with at the start of the story?
In many of the old dramas there is the "femme fatale" a stock character who exerts a life-changing influence upon the men "fatally" attracted to her. The Iliad by Homer has such a woman in Helen of Troy, the most beautiful woman in the world and the wife of Sparta's King Menelaus, whose brother is Agamemnon of Mycenae, the mighty commander in chief of the Achaean army. After Paris, a Trojan prince, steals Helen away, Agamemnon wages war on Troy.
The Iliad begins nine years after the Trojan War has started and first involves a quarrel between Agamemon and Achilles:
Agamemnon attacks the Danaans, who are allied with the Achaeans and sacks the town. He captures the daughter of a priest of the god Apollo named Chryses; when this priest offers to pay a huge ransom for his daughter, Agamemnon refuses. So Chryses appeals for help by praying to Apollo, and Apollo sends down a plague upon the Achaeans. This plague, having continued for ten days, becomes so damaging that Achilles summons the people together in order to learn what can be done to arrest the devastation.
Thereon the seer spoke boldly. "The god," he said, "is angry neither about vow nor hecatomb, but for his priest's sake, whom Agamemnon has dishonoured, in that he would not free his daughter nor take a ransom for her; therefore has he sent these evils upon us, and will yet send others. He will not deliver the Danaans from this pestilence till Agamemnon has restored the girl without fee or ransom to her father, and has sent a holy hecatomb to Chryse. Thus we may perhaps appease him."
However, the enraged Achilles will not agree to this unless he is allowed to take another prize in lieu of Chryses, a beauty named Briseis. He is so enraged that he tries to kill Agamemon, but, fortunately, he is stopped by the goddess Athena. Since his only reason for fighting other than to retrieve Helen, Achilles orders his army to return to their own land; meanwhile, Agamemnon sends his soldiers to retrieve Briseis. Because he realizes he has no choice, Achilles turns her over to the soldiers.
Angered by his situation, Achilles appeals to his mother, the goddess Thetis. He begs her to call upon Zeus for help in avenging him by aiding the Trojans in their combat against the Achaean army by destroying them.