Scattering theory provides a framework for understanding the scattering of waves and particles. This book presents a simple physical picture of diffractive nuclear scattering in terms of semi-classical trajectories, illustrated throughout with examples and case studies. Trajectories in a complex impact parameter plane are discussed, and it stresses the importance of the analytical properties of the phase shift function in this complex impact plane in the asymptotic limit. Several new rainbow phenomena are also discussed and illustrated. Written by Nobel Prize winner Roy J. Glauber, and Per Osland, an expert in the field of particle physics, the book illustrates the transition from quantum to classical scattering, and provides a valuable resource for researchers using scattering theory in nuclear, particle, atomic and molecular physics.