Books are designed to organize your library. This means that when you place a song into a book, it is a reference to that song, not a copy. What this means is that if you are viewing a book that you've created and remove a song by swiping right to left and tapping "Remove", the song is removed from the book but remains in your library.  You can access your entire library by going into the Songs Menu and tapping the Books button in the upper left to view the Books Menu and then tap All Songs.

Keep in mind that you should use sets for playing events, and books for organizing your library.  You can learn more about using both at the following video tutorial for books and sets.

When you swipe to delete a song from your books, it is only removed from the book. If you delete the song using another method such as the Delete Button in the Menubar of the Song Editor, or by tapping on the Edit button in the upper right corner and deleting the song using Multiselect, then yes, the songs will be deleted from your master library. You will want to ensure you use the Remove action, not the Delete action.

If you do accidentally delete a song, you can undelete songs that you've deleted by opening the Utilities Menu by tapping on the gear icon in the Menubar and choosing Tools and then Undelete Songs. Checkmark the songs you want to undelete and then tap Done to complete the process.