This book provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. This book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof. A bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. The book is aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences.