Agamemnon's first, and most profound, problem he creates for himself, and it eventually leads to his death at the hands of his wife, Clytemnestra. When the Greek fleet was anchored at Aulis, his councillors told him that he would have to sacrifice his daughter Iphigenia in order for the gods to grant fair winds to the Greek fleet. Although this idea appalls Agamemnon, he carries out the sacrifice of his innocent daughter, thereby insuring fair winds to take the Greek fleet to Troy's shores. Clytemnestra never forgives him, and even though she has taken a lover during Agamemnon's ten year absence during the war, when Agamemnon finally returns, she murders him. The god Apollo then orders Clytemnestra and Agamemnon's son Orestes to avenge his father's death, so Oreste's murders his mother, Clytemnestra. Orestes was hounded by the Furies for a long time until Minerva proved his innocence. The sacrifice of Iphigenia, then, set off a chain reaction that negatively affected Agamemnon and his family, as well as the entire Greek invasion force.
The sacrifice of an innocent daughter by her father was considered unnatural and an ill omen. In a culture subject to belief in omens and gods whose loyalties change according the their whims, the Greeks believed that if they appeased one god, they most likely created an enemy of another god, so Agamemnon's sacrifice of Iphigenia cast a shadow over the Greek enterprise before they even arrived on Troy's shores.
The Iliad takes place during the Trojan War, which set various Greek forces against the city of Troy. Some of the Greeks were led by King Agamemnon. Agamemnon commanded the forces of the Achaeans, who were in turn led by Achilles, the best soldier on either side of the war.
During one of the battles, Chryseis, the daughter of a Trojan priest, is captured and given to Agamemnon as a prize. Chryseis's father, Chryses, comes before Agamemnon with gifts, asking for his daughter's return; Agamemnon refuses and sends him away. Chryses is a priest of the god Apollo, and as punishment for Agamemnon's poor treatment of his priest, Apollo curses the Greeks with a plague. After consulting a prophet, Agamemnon learns that he must return Chryseis in order to end the plague. However, Agamemnon is not satisfied with giving up his captive, and so he orders that one of Achilles' captives, the woman Briseis, be taken from Achilles and given to himself. Achilles is outraged by this disrespect, withdraws his troops, and refuses to fight. Thus, thanks to Agamemnon's arrogance, the Greeks are weakened by the loss of some of their best troops.