This book is an introduction to a rapidly developing field of modern theoretical physics the theory of quantum transport at nanoscale. The theoretical methods considered in the book are in the basis of our understanding of charge, spin and heat transport in nanostructures and nanostructured materials and are widely used in nanoelectronics, molecular electronics, spin-dependent electronics(spintronics)and bio-electronics. The book is based on lectures for graduate and post-graduate students at the University of Regensburg and the Technische Universitat Dresden (TU Dresden).