An Introduction to Anomalous Diffusion and Relaxation Preface Integral Transforms and Special Functions Concepts in Diffusion and Stochastic Processes Random Walks Elements of Fractional Calculus Fractional Anomalous Diffusion Adsorption Phenomena and Anomalous Behavior Reaction Diffusion Problems Relaxation under Geometric Constraints I: Classical Processes Relaxation under Geometric Constraints II: Quantum Processes Index. This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects adsorption desorption phenomena memory effects reaction diffusion equations and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range including concepts in diffusion and stochastic physics random walks and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self contained text can be used as a reference source for graduates and researchers working in applied mathematics physics of complex systems and fluids condensed matter physics statistical physics chemistry chemical and electrical engineering biology and many others.