I came to recommend this as well. It's a study of the engineering and management efforts behind Apollo, and much more interesting and entertaining than that makes it sound. The section on how they developed the F-1 engines that powered the first stage of the Saturn V, including how they'd explode bombs inside the engine nozzle to be sure that it could cope with instabilities, is just one of dozens (hundreds?) of examples of how all the small pieces came together to accomplish their priorities, 'Man. Moon. Decade.'

An amazing book.