The story related in Malouf's Ransom is a part of a larger narrative originally related in Homer's Iliad, which is an epic Greek poem usually dated to around the 8th century BCE. It is one of the oldest works of Western literature and describes the last few weeks of the Trojan War, specifically the events during a fight between King Agamemnon and the famous warrior/demigod Achilles. The name comes from an alternate name for Troy (Illium), and although the poem doesn't cover all of the events of the Trojan War in real-time, over the course of the poem most of the war's significant events are retold.
The events of the war start decades earlier. An oracle prophesies that Priam's child Paris will bring about the destruction of Troy, so the family decides to abandon him on a hillside. Fortunately for Paris (but unfortunately for Troy), he is found and raised by a shepherd. Years pass, then one day, on Mount Olympus, Eris (the goddess of discord) presents the gods with a golden apple and claims that the apple should go to the most beautiful goddess. Three goddesses reach for it—Hera, Athena, and Aphrodite—but the gods can come to no conclusion. So they seek out a neutral party, who happens to be Paris. While all three goddesses promise him prizes if he chooses them, Paris is most convinced by Aphrodite's offer: the most beautiful woman in the world. So he chooses Aphrodite. Unfortunately, the most beautiful woman in the world happens to be married to King Menelaus of Sparta. When Paris and Aphrodite steal Helen from him, he decides to go to war. He goes to his brother, King Agamemnon, and together they rally all of Greece to fight to get Helen back. Troy is not willing to give Helen up. That starts ten years of war.
Achilles is considered the best warrior the Greeks have, but, as Ransom touches on, he withdraws from the war when he is offended by Agamemnon. His death story varies depending on the source, but most say that he is killed by Paris with an arrow to the heel (some versions say the arrow is guided by Apollo). He is cremated, with his ashes buried in the same urn as those of Patroclus. The fall of Troy happens not long after, with the hero Odysseus coming up with the famous Trojan Horse trick to let the Greeks into Troy. Homer's Iliad is followed by the epic poem The Odyssey, which is about Odysseus' journey home, and can also be read in conjunction with The Aeneid, which is a Roman epic poem about how the Trojan hero Aeneas escapes and goes on to found Rome.