* Renewing: This is the most common term. You can typically renew a book online, by phone, or in person at the library.
* Extending the due date: This is another way to say you want to keep the book longer.
* Requesting a hold: Some libraries let you request a hold on a book if it's already checked out, meaning you'll get it when the current borrower returns it. This effectively gives you more time with the book.
It's always best to check with your specific library to find out their policies and procedures for extending borrowing time.