The first thing you need to do is identify the Entities. All I see here is a list of Attributes. What are the attributes OF?
So, for instance, in your third group of text above, you seem to be leaning toward a MEMBER, a LOAN (of a book, I assume), a BOOK, and then it sort of falls apart.
Data modeling is not just an academic exercise. It's supposed to represent real-life objects and relationships. Take a step back and think about the real-life things about the hypothetical scenario that are of interest. It helps if you can draw from your own experience. Have you ever checked out a book from the library? Think back to that time. What were the things you saw? Well, obviously you were in a library. You were surrounded by books. You had a library card (or membership, whatever), and you wanted to borrow books (a loan from the library). Look at the book. It has an author who wrote it, and an ISBN number assigned to it, and a title. You borrow the book on a certain day, and have to return it by a certain day. Maybe the book you want isn't available. How do you reserve it? Is there more than one copy of it? Maybe at a different library? For the book, does it have only one author? Has the author written more than one book?
These are just a sampling of the questions you can ask. As you answer these questions, you can look at the attributes you have to select from, and decide which attributes belong to which entities.
Here's a freebie: Look at what appears to be your Author entity above. There should be no ISBN attribute in there...he's the author and doesn't depend upon his book for uniqueness. Now look at your other entities. See a pattern?
If you have your list of rules of normalization, keep them by your side as you go through this exercise...that way if you start to go off-track you can correct yourself.
Hope this helps. Good luck!
