This is really a very beautiful book on the mathematical structure of Quantum Mechanics. It is very useful for mathematically oriented students, because they can see functional analysis and spectral theory at work. Authors describe also less known parts (scattering states, many-particle systems, density matrices, Feynman path integrals, quasi-classical analysis, resonances, elementary parts of quantum field theory and renormalization group). The book can be also very useful for physicists. It shows which beautiful parts of mathematics are connected to the well-known parts of quantum mechanics. I must say that it was difficult to find a good textbook containing both physics and mathematics of quantum mechanics. I think that this book solves the problem how to teach quantum mechanics to mathematically oriented students in an optimal way. Thanks to the authors.