Whew! This will be an interesting forum thread!
Here's my answer:
The answer is 'it depends'.
It depends on whether you are interested in a specific class of U-boat. (e.g. for a Type VIIC the best single book is "Vom Original Zum Model: Ubootyp VII C" by Fritz Kohl, others are available for other classes)
If you are looking for the design and developmental history, then the best book is "The U-boat" by Eberhard Rossler.
If you are looking for operational history from inside the U-bootwaffe, then it's a little harder, but the books by Lawrence Paterson ("The First U-boat Flotilla", and "The Second U-boat Flotilla") are very good.
An excellent 2-book series on the U-boat war ("Hitler's U-boat War" by Clay Blair) is a treasure-trove of information on the Battle of the Atlantic as seen from both sides.
For a more general overall view of U-boats I would suggest "U-boats: The Illustrated History of the Raiders of the Deep" by David Miller.
There are hundreds of books on this subject, each with their own specific focus, some with a particular point-of-view (or sometimes outright bias), some without any photos, and some nothing but photos.
So what's your particular interest. We'll help you out!