I've managed to patch up damaged books before, but all my previous repairs have been much smaller, such as repairing a torn page or reattaching a loose cover with clear tape. In this case, I wasn't sure what was left of the book had enough structural integrity to be put back together. But I vaguely remembered reading about a book-repair technique described by Amy Dacyczyn (another of my household gods) in her Complete Tightwad Gazette, and I figured I had nothing to lose by attempting it before sending off to Amazon.com for a new copy.
The technique the Frugal Zealot (Amy Dacyczyn's nickname for herself in the book) describes is actually intended for reattaching the cover (or two separate covers) to an otherwise intact book. It works like this:
1) Cut a rectangle out of brown paper (such as a grocery bag) that's slightly longer than the spine of the book, and slightly more than twice as wide. (The book says to allow an extra half inch, but that's an approximation.)
2) Roll this paper into a tube and glue together the overlapping edges. (That's what the extra half inch is for.) Once it's dry, cut it to precisely the length of the spine.
3) Remove any old backing from the spine of the book. Apply white glue along the spine and let it dry.
5) At this point, the official technique is to glue a strip of cardboard to the exposed side of the tube, then glue a strip of "book cloth" over that and glue the overhanging edges of the cloth onto the book covers. But if you don't care about how the finished result looks, the simpler method is just to apply duct tape directly over the tube, overlapping it onto the covers by an inch or so, and smooth it down firmly.
I decided this had a chance of working with my damaged book if I carefully reassembled all the pages, squared them up precisely, and clamped the book together to hold them in place before attempting to attach the tube. With a bit of pressing and smoothing, we were able to get the tube to stick, as shown above. Once it was dry, I used two lengths of black duct tape to secure the tube to the covers, with only 1/4 to 1/2 inch of overlap (since the covers weren't the part most in danger of coming loose).