Formalism: Evolution Operators for Time Independent and Time Dependent Hamiltonian, Green'S Functions, Lippman-Schwinger Equation, the S- (Scattering) Matrix, the T-(Transition) Matrix for Reactive and Non Reactive Scattering Processes. Born Approximation. Application to Reactive Scattering: the Use of Quantum Scattering Theory for the Determination of Cumulative Reaction Probability, Quantum Mechanical Thermal Rate Constants, Transition States in Chemical Reactions, and of the Effects of Electromagnetic Field on Chemical Reactions. Applications to Nonreactive Scattering: Neutron Scattering from Solids: Neutron Diffraction, Inelastic Scattering and the Study of Lattice Vibrataions (Phonons) in Solids, Correlation Function, Recoilless Emission, Debye-Waller Factor. Molecular Beam Scattering from Solid Surfaces, Diffraction, Rainbow Scattering and Selective Adsorption.