Luna University

Luna University was a university located on Earth's Moon.

Luna University existed by 2643. A Professor Candy taught there at the time. (PROSE: Continuity Errors)

Bliss was an alumna of Luna University. (AUDIO: Echoes of War)

Circa 5123, River Song studied archaeology at Luna University in search of "a good man". (TV: Let's Kill Hitler)

Eventually, the Luna University granted River Song a doctorate in archaeology. The day her doctorate was awarded, the university was infiltrated by two Silents, Kovarian, and two members of the Church to re-kidnap River Song and use her in their scheme for killing the Eleventh Doctor. (TV: Closing Time)

Behind the Scenes
Kadiatu Lethbridge-Stewart was a student on a university placed on the moon in the 22nd century, although it is unknown if these two universities are the same (PROSE: Transit).