R. I. G. Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful. He goes on to show how the very suitability of Hilbert spaces for modeling the quantum world gives rise to deep problems of interpretation, and makes suggestions about how they can be overcome.
This book gave me a handle on the actual mechanics of QM like none other. Though it does not require a graduate degree in advanced mathematics, some amount of mathematical sophistication is required. The concepts are clearly explained; you just need to be able to follow along. I return to it often when I feel the need to review my vector mechanics.