At university vs. at a university vs. at the university

Greetings One Heart. Welcome to the forums.

Before addressing your specific questions, I’ll just note that “at university” is British English (BE). The AE (American English) equivalent is “at college”. Now on to your questions. I’ll leave the ones that are not AE to our BE colleagues.

I am working at university.

(Would not be said in AE.)

I am working at a university.

Correct. I am working. The place where I work is one specific, though unnamed, university. This is parallel to “I am working at a restaurant/government agency/auto dealership…”

I am working at the university.

Both speaker and listener know which university is referred to here. Although it is not named, the listener will have no doubts which university is the one where the speaker is working.

I am working in university.

(Not AE)

I am working in a university.

While it is not incorrect, it is far less common than “at a university”.

I am working in the university.

Again, it isn’t wrong, but it is a little odd in AE. We would say “at the university”.