This is the 223rd most frequent Turkish word.
üniversitesi
"Üniversitesi" means "university" in English.
The word 'üniversitesi' in this sentence is used as a possessive form ('University of Istanbul'), indicating an institution of higher education associated with the city of Istanbul.
İstanbul Üniversitasi Türkiye'nin en eski üniversitelerinden biridir.
Istanbul University is one of the oldest universities in Turkey.
Here, 'üniversitesi' (as in 'Ege Üniversitesi') identifies a university institution where a specific program was attended.
Ege Üniversitesi'nde biyoloji eğitimi aldı.
She studied biology at Ege University.
In this case, 'üniversitemizin' is the possessive form of 'üniversitesi', referring to the speaker's university and emphasizing its possession of a library.