I'm reading The Versions of Us by Laura Barnett. The story is based at Cambridge University and the ideas of "don", "master", and "brigadier" in the following paragraph puzzles me:
Vivian prefers to eat in college, but the last time Jim took her to the buttery, she had approached the dons’ table and engaged the startled master in conversation. It had taken him - a distinguished brigadier - almost half an hour to extricate himself.
The dictionary says "don" is "a teacher in a college or university; especially a teacher at Oxford or Cambridge University" and "master" is "a male teacher". Does that mean they are the same idea as "professor" except that "master" can only be used to refer to a male one? And what puzzles me most is brigadier. The dictionary defines "brigadier" as "a British army officer". But in this context, shouldn't this person be of a teaching position instead of a military one? Is "brigadier" also a title or rank of professorship?