In quantum computing, we witness an exciting and very promising merge of two of the deepest and most successful scientific and technological developments of this century: quantum physics and computer science. In spite of the fact that its experimental developments are in their infancy, there has already been a variety of concepts, models, methods and results obtained at the theoretical level that clearly have lasting value.These concepts, methods and results are the main subject of the book. Knowledge from two areas is of importance for understanding the basic developments in quantum computing: namely, quantum physics and theoretical computer science. The book provides elements of both, and concentrates on the presentation of concepts, models, methods and results mainly from a computing point of view. No previous knowledge of quantum mechanics is required. Supporting material for the book can be found on the Authors Web Site, http://www.fi.muni.cz/usr/gruska/foundations.html.