In a cave of Cyllene Maia became by Zeus the mother of the god Hermes. The story is told in the Homeric Hymn to Hermes.
After giving birth to the baby, Maia wrapped him in blankets and went to sleep. The rapidly-maturing infant Hermes crawled away to Thessaly, where by nightfall of his fitst day he stole some of Apollo's cattle and invented a lyre. Maia refused to believe Apollo when he claimed Hermes was the thief and Zeus then sided with Apollo. Finally, Apollo exchanged the cattle for the lyre.
Maia also raised the infant Arcas to protect him from Hera, who had turned his mother, Callisto into a bear.
Maia was identified in Roman mythology with Maia Maiestas (also called Fauna, Bona Dea (the 'Good Goddess') and Ops), a goddess who may be equivalent to an old Italic goddess of spring. The month of May was named for her; the 1st and 15th of May were sacred to her. Maia was associated with Vulcan, and on the first of May the flamen of that god sacrificed to her a pregnant sow, an appropriate sacrifice also for an earth goddess such as Bona Dea: a sow-shaped wafer might be substituted. The goddess was accessible only to women; men were excluded from her precincts.
In J. R. R. Tolkien's mythos, a Maia is one from the lesser kind of Ainur, beings of power which pre-date the creation of existence.
Maia is a city in Portugal.Reference
Harry Thurston Peck, Harper's Dictionary of Classical Antiquities, 1898
Encyclopaedia Britannica, 1911.