All around Rome there are public libraries where you can study or borrow books, movies and music for free. Open the MAP to discover where they are or search here a specific book on there database.
I’ve also just discovered a very alternative and indipendent library in the zone of Centocelle, called BAM (Biblioteca abusiva Metropolitana, which is something like: Metropolitan Unlawful Library). Here you can navigate on internet, play chess, or borrow a book for free. The place is definitely unconventional, also a bit dusty and with a lovely cat around. BAM on facebook. The address is: Via dei castani, 42