This book provides a detailed exposition of quantum scattering theory as applied to chemical physics. It includes the fundamental mathematics of scattering, details of how it applies to atom-molecule, molecule-molecule collisions, as well as collisions with surfaces. A variety of computational methods for solving scattering problems are presented. In addition, some discussion of fully quantal approximations is included. Both inelastic and reactive scattering are treated in detail. Both time-dependent and time-independent approaches to scattering theory and scattering computation are included. The book will reflect the research done over approximately 50 years by the author.