Is it permissible to replace old and worn-out books in the mosque library with new books of the same type, and what are the regulations or advice regarding dealing with the old books in the library?

It is permissible to change old books in the mosque and replace them with new ones if their condition necessitates it, just as the Rightly Guided Caliphs, such as Umar and Uthman, may Allah be pleased with them both, did. Whatever benefit can be derived from the old books should remain, and whatever cannot be utilized should be disposed of by burning or burying, to protect them from disrespect, by analogy with the Qur'anic manuscripts that were destroyed by burning during the era of Uthman, may Allah be pleased with him.