This monograph gives a comprehensive and up-to-date overview of soft and hard diffraction processes in strong interaction physics. The first part covers the general formalism (the optical analogy, the eikonal picture, high-energy kinematics, S-matrix theory) and soft hadron - hadron scattering (including the Regge theory) in a complete and mature presentation. It can be used as a textbook in particle physics classes. The remainder of the book is devoted to the "new diffraction": the pomeron in QCD, low-x physics, diffractive deep inelastic scattering and related processes, jet production etc. It presents recent results and experimental findings and their phenomenological interpretations. This part addresses graduate students as well as researchers.