If you're interested in general to diving into the Illiad, I'd highly recommend Achilles in Vietnam by Jonathan Shay.

Its nothing like the Song of Achilles (personally I didn't care much for it or it's YA nature though I can understand why it appeals to others), but if you're interested in a deeper understanding of the Illiad as well as exploring the social and cultural themes throughout it, I'd highly recommend it.

Its a non-fiction comparative work, analyzing how Homer explores topics such as trauma, morality, purpose, and self-worth by comparing it to his own studies (Jonathan Shay is a clinical psychiatrist) of PTSD in Vietnam Veterans. It's tragic and powerful, as it compares Homer's description of loss and PTSD to the modern day, showcasing how (to little surprise but interesting to read nonetheless) America often fails in providing support and care for not only veterans but those suffering from PTSD in general as well as discussing the consequences of suppressing emotion and mourning.

Highly recommend it, while having read the Illiad is helpful it's not required as any relevant passages being discussed have excerpts and background information provided