You can pass a book, back and forth, between devices and continue your reading as if you are passing a real book around (AirDrop must be enabled).
Inside a book, tap screen to show menu, and then follow the steps below:
1. Tap the export/share button
2. From the popup menu, select Book & Notes
3. Select the device that you want to airDrop the book
4. On the receving device, select Gutenberg to open the book
5. Continue reading on the same page on the receving device
Pass a book to the most desired device of the moment!