I purchased a book and it won't let me view it. The app automatically closes when I tap on the book

You've tried deleting the book and redownloading it via the Purchased tab in the app, and if that doesn't fix it tried closing the iBooks app via the phone's taskbar (Force an app to close in iOS - Apple Support) and/or tried a soft-reset/reboot of the phone (press and hold both the sleep and home buttons for about 10 to 15 seconds, ignore the ‘slide to power off’, after which the Apple logo should appear and it should reboot) ?

As you've marked my reply as having solved your problem I'm not sure whether you still have an issue or not.

If you do, then do any reviews for the book mention problems with it ? Or have you also tried downloading it on your computer's iTunes and syncing it ? Can you open other books in the app ?