This book introduces the scattering theory of non-relativistic systems, a standard tool for interpreting collision experiments with quantum particles at not too high energies. The aim is to explore the interaction between the particles and their properties. The authors cover the fundamentals of the theory through a detailed discussion of elastic scattering based on the stationary Schrödinger equation and the Lippmann-Schwinger equation. These discussions are complemented by the consideration of the time-dependent formulation of scattering theory. Selection rules for cross-sections based on symmetries, arising from the structure of the forces between the particles, and the scattering of spin-polarized particles are discussed. The foundations for the treatment of inelastic processes are laid and applied to three-body and nucleon interactions.