This is the 8025th most frequent Turkish word.
kütüphanesi
"The library of" or "his/her/its library."
In this sentence, 'kütüphanesi' refers to Ahmet's personal library or collection of books, indicated by the possessive suffix '-i'.
Ahmet'in kütüphanesi gerçekten onun için çok önemli.
Ahmet's library is truly very important to him.
Here, 'kütüphanesi' is used to denote the library of an institution, showing possession via the structure 'Üniversite+n+kütüphane+si'.
Üniversitenin kütüphanesi gece yarısına kadar açık kalıyor.
The university's library remains open until midnight.
In this context, 'kütüphanesi' identifies a specific library belonging to or associated with a certain place, 'mahalle' (the neighborhood), with the possessive form '-si'.