For those interested in the engineering details behind the whole flight, from engines, to power systems, guidance, navigation and computers, I would say my favourite book is

"How Apollo Flew to the Moon" by W David Woods https://www.amazon.com/Apollo-Flew-Springer-Praxis-Books/dp/...

A great book. Despite the cheesy-looking cover there is a lot of technical detail in this book.

It is also worth noting that there is now a second edition containing additional material. http://www.amazon.co.uk/Apollo-Springer-Praxis-Books-Explora...