Book nine is simply extraordinary. As Malcolm Willcock says, “In many ways it is the finest in the Iliad and is a self-contained whole.” To look at Book Nine from a bird’s eye view, we see Nestor propose that Agamemnon make amends with Achilles; Ag agrees and puts together a staggering shining ransom; Odysseus, Phoenix, and Ajax are selected to be part of the embassy that asks Achilles to return. Each man makes a speech and Achilles offers each a reply. To Odysseus he says that we will return home tomorrow; after Phoenix’s speech, his stance softens and he says that he will make his decision in the morning; after Ajax’s speech, he says that he will not assist the Achaeans until Hector begins to set fire to the Myrmidon ships; meaning that he won’t sail home and that he has ultimately decided in favor of a short and glorious life rather than a long life without undying fame. The results of the conversation are then reported back to Agamemnon.
An Introduction to Homer's Iliad Bk 9