The Library of Lunar Solace is a location that exists in an outside bubble dimension. This dimension is accessed within the pages of The Lunar Notebook. Technically the soul of any individual can enter the library, but many would be killed or driven insane by the process.
The Library acts as a repository of information gathered by Sirius Fulmaren before he died in 2108. The notebook was in the possession of Severa Fulmaren when last seen in 1200AD.
Because the Library is in its own bubble dimension, it does line up exactly with the timeline of Hyrule. This means that its Librarian, Bernard, does not necessarily experience events in the same linear fashion that the person holding the notebook does.