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The principal goal of this book is to provide state-of-the art coverage of the non-relativistic three- and four-body theories at intermediate and high energy ion-atom and ion-molecule collisions. the focus is on the most frequently studied processes: electron capture, ionization, transfer excitation and transfer ionization. the content is suitable both for graduate students and experienced researchers. for these collisions, the literature has seen enormous renewal of activity in the development and applications of quantum-mechanical theories. This subject is of relevance in several branches of science and technology, like accelerator-based physics, the search for new sources of energy and high temperature fusion of light ions. Other important applications are in life sciences via medicine, where high-energy ion beams are used in radiotherapy for which a number of storage ring accelerators are in full operation, under construction or planned to be built worldwide. Therefore, it is necessary to review this field for its most recent advances with an emphasis on the prospects for multidisciplinary applications.