You're probably wondering what kind of library that is, but I mean a place that is very quiet and people usually read books, or newspapers or do academic work, but there are no books or librarians there, it's just a peaceful place to read books. What's the word for that ?
A "reading room" is generally a quiet space for reading books. It may or may not contain books.
A "study" is generally a room for reading in a large home or estate. A study will often contain books.
A "study room" is generally a publicly accessible space at, for example, a library or school. The room itself usually does not contain books. Study rooms often have tables and a door, so that people can work together without disturbing people outside the reading room.
I think you are describing what is known as a “learning commons”. Wikipedia says:
Learning commons, also known as scholars' commons, information commons or digital commons, are educational spaces, similar to libraries and classrooms that share space for information technology, remote or online education, tutoring, collaboration, content creation, meetings and reading or study. Learning commons are increasingly popular in academic and research libraries, and some public and school libraries have now adopted the model. Architecture, furnishings and physical organization are particularly important the character of a learning commons, as spaces are often designed to be rearranged by users according to their needs.
Here are some images of such places: