This book gives an updated and detailed presentation of modern quantum-mechanical treatments and practical computational methods for dynamical processes of small molecular systems. The main emphasis is on the recent development of successful theories and computational methods for the reactive scattering process. Specific applications are given in detail for a number of benchmark chemical reaction systems in the gas phase and gas surface. Differing from traditional physics books focusing on abstract collision theory for elastic collisions, the book has been written in a fashion in which the development of general reactive or rearrangement scattering theory is accompanied by practical applications for realistic reaction systems.