The Danger Zone™

When you tap on the Edit button in the upper right corner of the books menu, you enter editing mode. When enabled, you can begin:

Sortin' Your Books Like You Actually Care

When the sort button in the lower left corner is set to a down arrow, you adjust the order of the books by draggin' the rows via the reordering handles on the right. When you're finally done messin' around, tap on the Done button in the upper right corner to save your changes (or don't—we're not your mom).

Deletin' Books (The Nuclear Option)

While you can delete books by swipin' from right to left over each row & tappin' on the Delete button which appears, you can also delete books in editing mode. Tap on the red minus circle to the left, & then tap on the Delete button that appears to nuke the book. This will not delete the songs in the book, just the book itself. (You're welcome.)

Editing Books, But Like... ADVANCED

You can perform some kinda fancy actions on books by tappin' on the name of the book when in edit mode. This will display the Action Menu that can be used to perform these actions (if you can figure out what they do).