Introduction Why yet another book on quantum mechanics?Quantum mechanics was born in the first experimental confirmations over the years.It is considered to be the fundamental physical paradigm,and has a wide range of applications,from cosmology to chemistry,and from biology to information sciences.It is one of the greatest intellectual achievements of the past century.As an effect of its invention,the veryc oncept of physical reality was changed and"observation,""measurement,""prediction,"and"state of the system"acquired a new and deeper meaning. Probability was not unknown in physics:it was introduced by Boltzmann in order to control the behavior of a system with a very large number of particles.It was the missing concept in order to understand the thermodynamics of macroscopic bodies,but the struc ture of the physical laws remained still deterministic.The introduction of probability was needed as a consequence of our lack of knowledge of the initial conditions of the sys- tem and of our inability to solve an enormous num mber of coupled non-linear differential equations. In quantum mechanics,the tune is different:if we have 10 radioactive atoms no intrinsic unknown variables decide which of them will decay first.What we observe experimentally andom process.The original explanation of this phenom enon ir quantum mechanics was rather unexpected.All atoms have the same probability of having decayed:only when we observe the system do we select which atoms have decayed in the past.In spite of the fact that this solution seems to be in contrast with common sense.it is the only possible one in the frame rk o the conventional interpretation of quan mechanics.Heisenberg,de Broglie,Pauli,Dirac,and many others invented a formalisn that was able to explain and predict the experimental data and this formalism led,beyond the very intention of the men who constructed it,to this conceptual revolution.Then,the old problem of the relatio among the observer and the obs ed object.discussed fo e seen from a new.completely different perspective. Once established,quantum mechanics became a wonderful and extremely powerful the diffe ials,the whole chemistry,became f the first bpredicted fom the theryind not only phenmenloa le deduced from experiments.The technological discovery that shaped the second half of last century,the transistor(i.e.the basis of all the modern electronics and computers)could not have been invented without a deep command of quantum mechanics. The advances of recent years have not only concentrated on the problems of interpreta- tion that could be(wrongly)dismissed as metaphysical by some people,considering themIntroduction Why yet another book on quantum mechanics? Quantum mechanics was born in the first quarter of the twentieth century and has received an enormous number of theoretical and experimental confirmations over the years. It is considered to be the fundamental physical paradigm, and has a wide range of applications, from cosmology to chemistry, and from biology to information sciences. It is one of the greatest intellectual achievements of the past century. As an effect of its invention, the very concept of physical reality was changed, and “observation,” “measurement,” “prediction,” and “state of the system” acquired a new and deeper meaning. Probability was not unknown in physics: it was introduced by Boltzmann in order to control the behavior of a system with a very large number of particles. It was the missing concept in order to understand the thermodynamics of macroscopic bodies, but the struc￾ture of the physical laws remained still deterministic. The introduction of probability was needed as a consequence of our lack of knowledge of the initial conditions of the sys￾tem and of our inability to solve an enormous number of coupled non-linear differential equations. In quantum mechanics, the tune is different: if we have 106 radioactive atoms no intrinsic unknown variables decide which of them will decay first. What we observe experimentally seems to be an irreducible random process. The original explanation of this phenomenon in quantum mechanics was rather unexpected. All atoms have the same probability of having decayed: only when we observe the system do we select which atoms have decayed in the past. In spite of the fact that this solution seems to be in contrast with common sense, it is the only possible one in the framework of the conventional interpretation of quantum mechanics. Heisenberg, de Broglie, Pauli, Dirac, and many others invented a formalism that was able to explain and predict the experimental data and this formalism led, beyond the very intention of the men who constructed it, to this conceptual revolution. Then, the old problem of the relations among the observer and the observed object, discussed for centuries by philosophers, had a unexpected evolution and now it must be seen from a new, completely different perspective. Once established, quantum mechanics became a wonderful and extremely powerful tool. The properties of the different materials, the whole chemistry, became for the first time objects that could be predicted from the theory and not only phenomenological rules deduced from experiments. The technological discovery that shaped the second half of last century, the transistor (i.e. the basis of all the modern electronics and computers) could not have been invented without a deep command of quantum mechanics. The advances of recent years have not only concentrated on the problems of interpreta￾tion that could be (wrongly) dismissed as metaphysical by some people, considering them