This book, which has evolved from the authors lectures at the University of Copenhagen and the University of Southern Denmark, draws on his experience as an active researcher in the interaction of charged particles with matter over more than forty years. The emphasis is on the theoretical description of fundamental phenomena, and much attention has been given to classic topics such as: Rutherford scattering; the theory of particle stopping as developed by Bohr, Bethe, Bloch and Lindhard; the statistical description of energy loss as developed by Bohr, Bothe, Williams and Landau; and numerous more recent developments. An attempt has been made to provide at least one complete derivation of a theoretical description for all central aspects. The presentation is intended to respect the ideas of the original authors, but much effort has been invested in establishing a unified and appealing notation consistent with present-day standards. It is intended that this volume will satisfy a long-standing need for a textbook suitable for introductory courses on interactions of charged particles with matter for students of physics, chemistry and related fields at the graduate and postgraduate level. In order to make it useful for researchers in materials science, electrical engineering, medical technique and other application areas in science and engineering, a large number of appendices has been added with background material that should be familiar to physicists but not necessarily to others. Chapters 1-5 are predominantly tutorial, while chapters 6-9 develop topics leading to the frontiers of research.