From a strictly amateur interest in gas turbines, and in chopping them up to make furniture, I've been reading up on their theory. Here are some of the books I've found useful.
This is a great book for the amateur and historian. Taking a very qualitative approach, rather than the dry quantitative approach of some others, this gives a great grounding. It's really two books; the first is a spinner-to-jetpipe explanation of the machine. The second is a history from Whittle to the present. In Gunston's typical manner, it's a broad history, looking equally at all makers and not ignoring the Soviet developments.
Despite the less-formal technical slant, this is a great explanation of the theory.
If you read only one book on gas turbines, make it this one
Supposedly a book on building your own gas turbine, suitable for RC model aircraft, it has a lot more to offer. The description of gas dynamics is ne of the most approachable I've seen. It also presents a good argument for why the centrifugal compressor is the most approriate type for smaller engines.
This book takes a "fitter's view" of the jet engine. It's an easy read, and beautifully illustrated with large clear line drawings on each page.
There is little historical information in this book, which is a pity. Clearly its target is the present, not the past. Each chapter is introduced with an old photograph and a current sectioned view, but that's as far as it goes. Only Rolls-Royce engines are described, although that includes all of the previous British engine builders. I'd very much have liked to see a timeline, or even a current range of their engines.