This authoritative volume is the first to present a comprehensive and up-to-date review of our new understanding of accretion disks around black holes. Interest in black hole accretion disks has undergone a renaissance in recent years because of developments in three complementary areas: theoretical modeling of relativistic plasmas, numerical simulations with supercomputers, and observational tests now possible using new observatories such as the Japanese X-ray satellite, ASCAR. This volume presents review papers on all these topics from leading world authorities who gathered at an international conference in Reykjavik, Iceland. The authors are M. Abramowicz, P. Artymowicz, A. Brandenburg, G. Bjornsson, P. Charles, A. Fabian, J. Krolik, J.-P. Lasota, G. Madejski, R. Narayan, I. Novikov, J. Papaloizou, J. Poutanen, J. Pringle, M. Rees, E. Spiegel, R. Svensson, P. Witta. This timely volume provides an up-to-date review of the theory of black hole accretion disks for graduate students and researchers in astrophysics and theoretical physics.