[briankirby]

Personally, I find Nielsen and Chuang (Mike and Ike as it's affectionately referred to in the field) to be a good reference, but not great for learning the topic the first time. It's also expensive. I think that Rieffel and Polak [0] is a little easier to follow, and surprisingly thorough for an introductory book. Note, there is no reason to buy a book though, as John Preskill has his notes online [1], which I often see cited in published manuscripts.

[0] https://www.amazon.com/Quantum-Computing-Introduction-Engine... (Here is a much shorter document by the same authors written explicitly for non experts: https://arxiv.org/abs/quant-ph/9809016)

[1] http://www.theory.caltech.edu/people/preskill/ph219/