I am a rotating equipment engineer looking after natural gas compression assets, the following might be useful:
I have just obtained Volume 3 of Forsthoffers Rotating Equipment Handbook Series entitled 'Compressors'. If I had to have one book dealing with the basics of Compressors, this would be it (despite the dodgy grammar). Good all round description of compressors, although a lot of bias towards centrifugals.
I also make very good use of 'Compressor Performance: Aerodynamics for the User' by M.Theodore Gresh - don't let the title put you off, its got good clear explanations of compressor theory, thermodynamics and constructions that can be followed by just about anybody
Both of these books were written by people who have spent a lot of time actually working with compressors and their experience clearly shows.
I am considering buying Compressors 3rd Edition by RN Brown - it goes into a bit more depth on the theory side.
In contrast, avoid anything by Boyce (e.g. Centrifugal Compressors: a Basic Guide). This book is truly awful - a book by an academic for other 'heads in the clouds' academics - no relation to the real working world - a lot of the material is 'cribbed' from other sources and my quite new edition is poorly printed (i.e. amateurish quality diagrams)- clearly written by someone who is more at home in a classroom and who probably wouldn't recognise a compressor if he fell over one. In short, a huge waste of money.
Similarly, avoid 'Compressor Handbook' by Hanlon.
Check Amazon for purchase