Double check with your library, but the best app to get to view public library books is the app Overdrive (free in the App Store). With a library card and an account, you can get virtually any library's books. You just need to make sure your library uses the Overdrive system (most do).
The app BlueFire Reader can also help you get and read library books.
They are both the same in that you have to authorize them with your Adobe Digital Editions password. But, once that is done, then you are good.
Hope this helps.
Marilyn