During the last two decades the theory of ion-atom collisons, and particularly of charge-exchange reactions has advanced rapidly to the point where existing texts are no longer suitable as an introduction to the subject. This book aims to remedy the situation by providing an account of modern theoretical methods used to study the interaction of positive ions with atoms (or ions), concentrating particularly on charge exchange reactions. These reactions cannot be studied in isolation, and it is necessary to consider, to some extent, the whole range of ion-atom collisions leading to elastic scattering, excitation, and ionization. The material is presented at a level suitable for beginning research students and is self-contained, but assumes a knowledge of undergraduate quantum mechanics and atomic physics. It should also be useful for experimentalists who wish to assess the status of theoretical treatments of those collision processes in which they are interested.