Because of its subject matter, both the teacher and the students will likely end up making a lot of references to classical mythology. Edith Hamilton's Greek Mythology may be one book that students will recall when reading The Iliad, as well as Homer's The Odyssey, Virgil's The Aeneid, and other works from Greco-Roman antiquity.
The conclusion of the Trojan War is made known in other Greek stories which scholars group under the rubric of "the Epic Cycle". By the time of the Roman Empire, these stories had already been almost entirely lost, and what has survived to the present day are merely fragments and summaries. However, later works by other authors (such a Quintus of Smyrna's ...