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The quantum measurement problem is considered one of the most fascinating and challenging topics in physics, both theoretically and experimentally. It involves deep questions and the use of very sophisticated and elegant techniques. After analyzing the fundamental princples of quantum mechanics and of the Copenhagen interpretation, this work reviews the most important approaches to the measurement problem and reformulates the "collapse of the wave function" by measurement, as a dephasing process quantitavely characterized by an order parameter (called the decoherence parameter), according to the many-Hilbert-space approach to the problem. The book deals with not only the measurement processes (including imperfect measurements), but also related interference and mesoscopic phenomena - by means of general arguments - of solvable models and of numerical simulations. The quantum Zeno effects and the issue of the irreversibility are also discussed.