In the course of teaching quantum mechanics at undergraduate and post-graduate level, we have come to the conclusion that there is another original book to be written on the subject. The abstract setting foreseen by Dirac and the geometric view pioneered by von Neumann are finding new realizations, leading to further progress both in physics and mathematics, while the applications to quantum computation are opening a new era in modern science. Our emphasis is mainly on structural issues and geometric ideas, moving the reader gradually from the concepts of classical mechanics to those of quantum mechanics, but we have also inserted many problems for students throughout the text, since the book is written, in the first place, for advanced undergraduate and graduate students, as well as for research workers.

The overall picture presented here is original, and also the parts in common with a previous monograph by some of us have been rewritten in most cases. The analysis of waves and particles (Chapter 3), the treatment of symmetries in quantum mechanics (in particular, the first half of Chapter 10), the assessment of modern pictures of quantum mechanics (Chapter 12) have never appeared before in any monograph, to the best of our knowledge. The material on experimental foundations is rather rich and it cannot easily be found to the same extent elsewhere. Our presentation of classical mechanics is original and the choice of topics is motivated by the subsequent development of quantum mechanics, expecially wave equations, Poisson brackets and harmonic oscillators.