Arete is the term given to excellence or honour that was won by heroes by achieving feats of great skill or bravery. Arete is a central theme to this book as the warriors all are striving to gain arete during the Trojan War and seek to show themselves as being more honourable and excellent than other soldiers.
Particularly interesting to this debate is the conflict between Achilles and Hector, and which gains more arete. You might want to consider yourself which of these two characters gains more arete than the other.
Certainly, Hector seems to be a stereotypical hero. He shows massive loyalty and bravery in the face of unfavourable odds and is self-sacrificing to the extreme. We can argue that he most definitely gained arete before his death. Achilles, on the contrary, does not show himself to be the same kind of hero. For a large proportion of this text he is absent from the battlefield, withdrawing his services because of what Agamemmnon did to him through the woman he won, Briseis. He spends more time throwing tantrums over the loss of his honour and ironically lessening his arete. Although in the end he is spurred into battle and defeats Hector, it is only to gain revenge that Achilles does this.
Thus which characters gain arete and how is a key question and theme that runs throughout this novel and helps us to consider how characters are compared and contrasted with each other.