Some of them were built in the middle ages.
Some days ago a remarkable photo series was published by the state-run Hungarian news agency MTI.
Its photographer (Csilla Cseke) traveled around the country and took pictures of the most beautiful or significant libraries in the country.
Most of them were build in the 19th century which was a golden age of the Hungarian history but some are much older.
Anyway, you can visit these places as a tourist as well.