is the author of both the Illiad and The Odyssey. Homer doesn't really deal with Amazons. However, characters, such as Medea and Achilles,crossover into relevant myths, poems and plays. The Illiad is just a section of the Trojan war, but the Amazons are mentioned in association with both the war and Achilles in other texts.

In the classical period of Greek literature, Homer was the primary representative of what we know as epic. The figure of Homer as a poet of epic was considered to be far older than the oldest known poets of lyric, who stemmed from the archaic period. It was thought that Homer, acknowledged as the poet of the Iliad and the Odyssey, stemmed from an earlier age. Herodotus (second half of the fifth century BCE) says outright that Homer and Hesiod were the first poets of the Greeks (2.53.1–3). It does not follow, however, that the myths conveyed by the poetry of Homer and Hesiod are consistently older than the myths conveyed by the poetry of lyric. In fact, the traditions of Greek lyric are in many ways older than the traditions of Greek epic, and the myths conveyed by epic are in many ways newer than the myths conveyed by lyric.

Homer and Greek myth Nagy, Gregory.  In The Cambridge Companion to Greek Mythology, edited by Woodard, Roger D, 52-83. Cambridge: Cambridge University Press, 2008.