This book is devoted to the theory of quantum measurements, an area that recently has attracted much attention because of its new applications for quantum information technology. The phenomenon of decoherence of a measured system is investigated and simple techniques for the description of a wide class of measurements are developed. An individual continuously measured (decohering) system is presented by an effective complex Hamiltonian which supplies a phenomenological theory of gradual decoherence. The work, which features a clear presentation of physical processes leading to quantum measurement (decoherence) and simple mathematical formalisms, concentrates on the physical nature of quantum measurements and the behaviour of measured (open) quantum systems, but conceptual problems are also treated. The analysis of interrelations between different approaches to quantum measurement is given. The methods developed in this volume are applicable for the description of individual continuously measured (decohering) systems, not only to a whole set of such systems. Audience: This work will be of interest to both researchers and graduate students in the fields of quantum mechanics, metaphysics, probability theory, stochastic processes, the mathematics of physics and computational physics.