There are 111 Pre-War Books. If turned in to the Brotherhood, they give you back 100 bottlecaps and you get 10 XP. It's in the unmarked quest Yearning for Learning. See here for the Pre-War Book locations.
The 111 number only counts for the true Pre-War Book number, there are far more false Pre-War Books in the wasteland, and the difference can be told in the icon on your inventory. It is said Crazy Wolfgang sells false Pre-War Books until you fully invest in his stock, then he carries real ones, however, this has been tested to be incorrect.