Professor

Professor was a title given and used by a variety of people throughout history, usually (though not limited to) peoples of university educated pedigree.

Ace referred to the Doctor as Professor throughout her early association with him (DW: Dragonfire et al) and often continued to refer to him as 'Professor' in a friendly manner several years later. (NA: Happy Endings)

In the year 100,000,000,000,000, Yana was given the title of professor, despite there being no universities for over a century. (DW: Utopia)

Specific professorships

Bernice Summerfield originally faked her qualifications as a professor of archaeology; however she did eventually obtain a professorship. (NA: Love and War, Return of the Living Dad)

River Song introduced herself as a professor at a university of archaeology. (DW: Silence in the Library)