Question

Who or what is the Muse that Homer references in the invocation?

Answer 1

Answer: If it's The Odyssey, The Muse is unnamed. The Muse is the spirit or goddess who gives the poet his words and inspires the poet to tell the story.

Explanation:

In about line 17, "Of these adventures, Muse, daughter of Zeus, tell us in our time. . ." we find out she is a daughter of Zeus: Greek Mythology lists nine muses among them Clio, Eurterpe and Kalliope.  But it is uncertain which one Homer is invoking.

Athena, a major player in the Odyssey, is also a Daughter of Zeus- sprung full-panoplied from his brow-- is not a Muse.