This volume presents a state-of-the-art account of the theory and applications of integral equations of convolution type, and of certain classes of integro-differential and non-linear integral equations. An extensive discussion of some open questions and of various important directions for further research is also presented. The book has been written so as to be self-contained and includes a list of symbols with their definitions. For users of convolution integral equations, the volume contains numerous inversion tables which correspond to the various convolutions and intervals of integration. The convolution integral equations which are considered arise naturally from a large variety of physical situations and it is felt that the types of solutions discussed should be useful in many diverse disciplines of applied mathematics and mathematical physics.