I've read some of Caroline Alexander's books before including the brilliantly left-field depiction of polar exploration, Mrs.Chippy's Last Expedition.
The war that killed Achilles (Guardian review) is a brilliant exegesis of The Iliad that attempts to reclaim the story as one about the dreadful waste of war. Achilles is envisaged as a rebellious warrior as eager to return home to obscurity as he is to vengefully fight for glory. Homer is the poet that humanises the fallen victims of a war on both sides and sees in the conflict the fall of both Greek and Trojan.
There are lots of interesting observations throughout the book. Achilles mother Thetis is an immortal, already estranged from her mortal and aged husband and soon to lose her son. Her grief will be all the greater for being immortal and eternal, her son is short-lived but the grief of his death must be born forever.
Hector decides to save his life and flees Achilles, only to be tricked by the gods into facing him and subsequently dying.
Alexander is also adept at invoking the fate and tragedy of the women of the Iliad. Taken as prizes and put to the service of the murderers of their family, removed to foreign lands and utterly powerless.
Ultimately she feels that the true message of the Iliad has been usurped and this is an attempt to re-position it as the ultimate and complete tragedy, corrupting and destroying everyone who takes part in it, including the gods themselves.