Hi, Izzi3!
Thanks for using the Apple Support Communities. After reading your post, I understand you downloaded a free book from the iBooks Store, and later removed it from your device. Now, you still see it in your library but no longer wish to. I have a lot of books in iBooks myself, so I know how important managing what you see (and what you don't) is, and am happy to help!
Any purchases (even free downloads) you make in the iBooks store (as well as in the iTunes Store and App Store) are permanently tied to your Apple ID. If you no longer wish to see specific content in your library, though, you are able to hide purchases following the instructions under the "Hide your purchases" section of the article below.
Hide and unhide iTunes Store, App Store, or iBooks Store purchases
Cheers!