This book serves as an introduction both to classical scattering theory and to the time-dependent theory of linear equations in mathematical physics. Hibert space methods are used to develop the latter theory in such a way that the asymptotic behaviour of large time can be discussed; among other topics discussed are the proof of the existence of wave operators, some of the special equations of mathematical physics (Maxwell equations, the linear equations of elasticity and thermoelasticity, and the plate equation), exterior boundary value problems, radiation conditions, and limiting absorption principles. The background knowledge required for a full understanding of the concepts discussed here is presented in the second chapter; there is also an extensive reference list, which enables readers to increase their familiarity with topics which are not central to the subject under discussion. The material in this book is drawn from courses given by Professor Leis in West Germany, and in Great Britain where he was a visiting Professor. These courses were given to graduate students of Mathematics and Physics, and it is for these people in particular that the book is intended, although it will also prove useful to their teachers, and to those carrying out detailed research in the field.