So... it's called "Life at University", instead of "University Life".
And... that is honestly a red flag for me.
Both "life at university" and "university life" are grammatically correct and commonly used phrases. The choice between them depends on personal preference and the context in which you are using the phrase.
"Life at university" emphasizes the experience of being a student and all the aspects that come with it, such as academic pursuits, social interactions, and personal growth. It suggests that university is a central aspect of one's life and focuses on the individual's perspective.
"University life" refers to the overall experience and environment of being at a university. It encompasses various aspects of the university as a whole, including academic programs, campus culture, extracurricular activities, and the overall atmosphere. This phrase takes a broader perspective and emphasizes the collective experience of all individuals within the university community.