The principal goal of this book is to provide state-of-the-art coverage of the non-relativistic three-body theory of high-energy ion-atom collisions. The main aspects of generalizations to tissue-like molecular targets, such as water, are also outlined. The focus is on the most frequently studied two processes, single electron capture and ionization. For the studied collisions, the literature has seen enormous renewal of activity in the development and applications of quantum-mechanical theories. This subject is of great relevance in several branches of science and technology, such as accelerator-based physics, research in new sources of energy and high temperature fusion of light ions. Other important applications are in the life sciences and medicine, where high-energy ion beams are used in cancer therapy. Therefore, it is necessary to present this field in its full capacity with the primary emphasis on realistic prospects for multidisciplinary applications, especially in radiotherapy.The present book is aimed to match the growing demand from theory and experiment, as motivated by high relevance for fundamental physics as well as for other fields such as fusion, medicine, etc. The overall emphasis in this book is not on compilation of cross sections, but rather on collisional mechanisms involving ions and atoms at high non-relativistic energies. The principal outlines for extensions of the analyzed theories' molecular targets (e.g. water) are also presented for the needs of hadron therapy.