An inquisitive reader asks where she might find versions of the Greek myths in ancient Greek poetry.
The first answer to that question is just about everywhere.
As near as anyone can figure, the normal setting for a Greek myth in its earliest form was in poetry. In the early days of Greek civilization, poetry was an easy way of telling stories. Greek poetry has a regular, memorizable structure, Greeks grew up with it in their ear, and if we believe some scholars, it could be improvised in performance, especially by trained reciters. Scholars call this phenomenon the "oral tradition."
The details of this tradition will be argued by scholars for generations to come. The essential for now is that most of the best-known Greek myths exist in poetry form, starting with the Iliad and the Odyssey, which were composed in the 8th c. BC.
Prose versions of the myths did not start to come into existence, scholars believe, until the 5th c. BC, when philosophers started to catalogue and study mythology.
Here is a list of some ancient Greek poems with mythological material in them. In the books bar to your left and down, you'll find recommended editions for these poems.
The Theogony and Works and Days, by Hesiod. Foundational poems for Greek mythology, the Theogony is a genealogy of the gods, plus other material, such as Prometheus' stealing of fire from Zeus. Works and Days is primarily a poem about farming and the ancient calendar, but you'll also find the story of Pandora there.
The Homeric Hymns. A must read-- BwP says five stars. These are stories about the gods, and though they are called "hymns," they have a certain irreverence which is irresistible. You'll find the story of Persephone and Demeter here, the story of Hermes' birth and the theft of the cattle of Apollo, the story of how Aphrodite fell in love with a human being, and plenty more.
Pindar's Pythian IV and Apollonius Rhodius' Argonautica. Early (5th c. BC) and late (3rd c. BC) versions of Jason and the Golden Fleece. Pythian IV is weird and allusive, because it was composed as a performance in dancing and singing for a victor at the Pythian games in Delphi-- sort of the first music video. The Argonautica is not really my cup of tea, but it has lots of detail about the trip Jason took to get the Fleece.
All Greek tragedy is poetry, and almost all surviving Greek tragedy draws from myth for its plots and characters.
This is to get you started. There' s more, but not as accessible.