E-R diagram is not easy for me to draw, so you can convert it according to the following relational model.

List of books (title, ISBN, author, unit price, publishing house) Main code: ISBN.

Reader list (library card number, name, gender, unit, category number) main code: library card number, external code: category number.

The main code of the library slip (library card number, book number, end date and book return date): library card number+book number+end date.

Foreign code: library card number, book number

Loan authority table (category number, name, maximum loan amount and loan term) Primary code: category number.

Draw an E-R diagram accordingly, and pay attention to one-to-many and many-to-many directions.