Translation:I am reading a book in the library.
Because that suggestion is not proper English sentence structure/grammar.
Nearly -- it's der Bibliothek: der due to dative, and Bibliothek with a capital B because it's a noun.
die Bibliothek became der Bibliothek because it is dative case with switchable two-away preposition 'in'. when the sentence with 'in' describing movement from one to another location, it will be accusative. and when the sentence describe something without shifting place, it will be dative.
in case anyone get confused with preposition just like I am : )