This book highlights selected topics of standard and modern theory of accretion onto black holes and magnetized neutron stars. The structure of stationary standard discs and non-stationary viscous processes in accretion discs are discussed to the highest degree of accuracy analytic theory can provide, including relativistic effects in flat and warped discs around black holes. A special chapter is dedicated to a new theory of subsonic settling accretion onto a rotating magnetized neutron star. The book also describes supercritical accretion in quasars and its manifestation in lensing events. Several chapters cover the underlying physics of viscosity in astrophysical discs with some important aspects of turbulent viscosity generation. The book is aimed at specialists as well as graduate students interested in the field of theoretical astrophysics.

The editor, Nikolai Shakura (b. 1945), is the head of the Relativistic Astrophysics Department of the Sternberg Astronomical Institute, where he has also been working all his life after graduating from the Lomonosov Moscow State University. In the early 70-s N.I.Shakura in collaboration with R.A.Sunyaev developed the fundamental theory of disc accretion onto relativistic compact stars. Even before the era of systematic X-ray observations of the sky, these authors predicted almost all observational manifestations of accreting neutron stars and black holes, which were later brilliantly confirmed by observations. Their work has been cited more than 8000 times. Overall, Nikolai Shakura is the author of more than 200 publications on accretion discs and considered a well acknowledged authority in the field.

Pavel Abolmasov is a postdoctoral fellow at Tuorla Observatory, University of Turku, Finland and a researcher (on leave) at the Sternberg Astronomical Institute of Lomonosov Moscow State University, Russia.

Anna Chashkina is a PhD student at Tuorla Observatory, University of Turku, Finland and a researcher (on leave) at the Sternberg Astronomical Institute of Lomonosov Moscow State University, Russia.

Linnea Hjalmarsdotter is a former researcher an the Sternberg Astronomical Institute  of Lomonosov Moscow State University, Russia.

Alexandra Kochetkova is a former researcher at the Sternberg Astronomical Institute of Lomonosov Moscow State University, Russia.

Galina Lipunova is a researcher at the Sternberg Astronomical Institute of Lomonosov Moscow State University, Russia.

Konstantin Malanchev is a researcher at the Sternberg Astronomical Institute of Lomonosov Moscow State University and an associate professor at the National Research University Higher School of Economics, Moscow, Russia.

Konstantin Postnov is a professor at the Faculty of Physics of Lomonosov Moscow State University and at the National Research University Higher School of Economics, Moscow, Russia.

Dmitry Razdoburdin  is a researcher at the Sternberg Astronomical Institute of Lomonosov Moscow State University, Russia.

Vyacheslav Zhuravlev is researcher at the Sternberg Astronomical Institute  of Lomonosov Moscow State University, Russia.

Preface.- The Standard Model of Disc Accretion.- The Properties of Spherical Geodesics in the Kerr Metric.- Relativistic Standard Accretion Disc.- Relativistic Twisted Accretion Disc.- Structure of Accretion Discs in Lensed QSOs.- Transient Dynamics of Perturbations in Astrophysical Discs.- Quasi-spherical Subsonic Accretion onto Magnetized Neutron Stars.- On the Properties of Velikhov-Chandrasekhar MRI in Ideal and Non-ideal Plasmas.