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This book gives a systematic description of collision theory within the framework of non-relativistic quantum mechanics. However, the final expressions obtained can also hold for particles with spin and under relativistic conditions. The general theory is formulated for two elementary particles, for the scattering of an elementary particle with a bound system of elementary particles, and for the scattering process for a three-particle system (Faddeev's theory). In addition, the scattering problems are considered using exact and approximation methods.