Myths generally do not have known authors. When mythology is transmitted by an oral tradition, it just becomes a kind of common knowledge, rather than the work of a specific author. However in the case of Greek mythology, some of it is attributed to an author named Homer. Even in this case, it is believed that the work of many different people was later attributed to Homer, who may or may not have been a real person.
The two most well known are hesiod and homer.
The myths were the ancient Greek religion, not works of one or more writers. In their works Homer and Hesiod tell us about those myths, later also Roman writers as Ovid and Virgil.
Greek myths didn't have a specific author. They were religious folk tales that wee spread verbally long before they were ever written down.
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