Achilles is often presented as the hero of the novel, but more than often Hector is presented in a kinder light. Which one do you feel best fits the archetype of the hero? Do they both?
The first paragraph of the book is the author Homer invoking the muses' to speak of Achilles wrath. Why do you think he chose to start the novel with that?
Analyze the behavior of the gods throughout the book. Who sides with whom? How do the different gods behave? Is this true to their appearance in other mythology?
Notice how the book mirrors itself; the first half shows the Trojans beating back the Argives, while the second half shows the Greeks overcoming Troy's forces. Was this intentional?
The war is often accredited to the seizure of Helen by Paris, though the death tolls make that seem ridiculous. Do you think some of the characters are fighting perhaps for other intentions or motives?