2 Introduction to be beyond experimental tests.In the last 30 years,the whole complex of problems con- nected to quantum mechanics and the meaning of measurements started to be studied from new perspective.Real not ony Gedanker experiments began to be done on some of the most elusive properties of quantum mechanics,i.e.the existence of correlations among spatially separated systems that could not be explained using the traditional concept of probability.The precise quantum mechanical meaning of measurements started to be ana- lyzed in a more refined way (e.g.quantum non-demolition measurements were introduced) and various concepts from statistical mechanics and other fields of physics began to be used. This is not only an academic or philosophical problem.The possibility of construct- ing a quan um computer,which would improve the speed of present day c mputers by ar incredible factor,is deeply rooted in these achievements.It is now clear that a quantum computer can solve problems,which on conventional computers take a time exploding as exponent of some parameter (e.g.the factorization into primes of a number of length N).in a time which is only a polynomial in N.The technical problems to be ove come in constructing a quantum computer are not easy to solve,but this result has a high conceptual status,telling us how deeply quantum mechanics differs from classical mechanics.Another quantum-information puzzling phenomenon,ie.teleportation,has been e proved experimemtally to eiand it isa very active area of experimenta res The arguments above explain why this new situation imposes the necessity to treat this field in a new way.The idea of writing this book came to one of us in 2000:it has taken more than eight years to accomplish this challenge Outline The book is divided into four parts: I Basic features of quantum mechanics Part I deals with the basic framework of the theory and the reasons for its birth.Fur thermore,starting from the fundamental principles,it explains the nature of quantum observables and states,and presents the dynamics of quantum systems and its main examples. ⅡMore advanced topics In Part II we introduce angular momentum,spin,identical particles,and symmetries. Moreover,we give a special emphasis to the quantum theory of measurement. IⅢMatter and light We devote Part II to some of the most important applications of quantum theory: approximation methods and perturbation theory,the hydrogen atom,simple molecules. and quantum optics. IV Quantum information:state and correlations Finally,we deal with the most recent topics:the quantum theory of open systems,state 2 Introduction to be beyond experimental tests. In the last 30 years, the whole complex of problems con￾nected to quantum mechanics and the meaning of measurements started to be studied from a new perspective. Real, not only Gedanken experiments began to be done on some of the most elusive properties of quantum mechanics, i.e. the existence of correlations among spatially separated systems that could not be explained using the traditional concept of probability. The precise quantum mechanical meaning of measurements started to be ana￾lyzed in a more refined way (e.g. quantum non-demolition measurements were introduced) and various concepts from statistical mechanics and other fields of physics began to be used. This is not only an academic or philosophical problem. The possibility of construct￾ing a quantum computer, which would improve the speed of present day computers by an incredible factor, is deeply rooted in these achievements. It is now clear that a quantum computer can solve problems, which on conventional computers take a time exploding as exponent of some parameter (e.g. the factorization into primes of a number of length N), in a time which is only a polynomial in N. The technical problems to be over￾come in constructing a quantum computer are not easy to solve, but this result has a high conceptual status, telling us how deeply quantum mechanics differs from classical mechanics. Another quantum-information puzzling phenomenon, i.e. teleportation, has been recently proved experimentally to exist and it is a very active area of experimental research. The arguments above explain why this new situation imposes the necessity to treat this field in a new way. The idea of writing this book came to one of us in 2000; it has taken more than eight years to accomplish this challenge. Outline The book is divided into four parts: I Basic features of quantum mechanics Part I deals with the basic framework of the theory and the reasons for its birth. Fur￾thermore, starting from the fundamental principles, it explains the nature of quantum observables and states, and presents the dynamics of quantum systems and its main examples. II More advanced topics In Part II we introduce angular momentum, spin, identical particles, and symmetries. Moreover, we give a special emphasis to the quantum theory of measurement. III Matter and light We devote Part III to some of the most important applications of quantum theory: approximation methods and perturbation theory, the hydrogen atom, simple molecules, and quantum optics. IV Quantum information: state and correlations Finally, we deal with the most recent topics: the quantum theory of open systems, state