This monograph describes the behaviour of cosmic rays in the magnetosphere of the Earth and of some other planets. Recently this has become an important topic both theoretically, because it is closely connected with the physics of the Earths magnetosphere, and practically, since cosmic rays determine a significant part of space weather effects on satellites and aircraft. The book contains eight chapters, dealing with The history of the discovery of geomagnetic effects caused by cosmic rays and their importance for the determination of the nature of cosmic rays or gamma rays The first explanations of geomagnetic effects within the framework of the dipole approximation of the Earths magnetic field Trajectory computations of cutoff rigidities, transmittance functions, asymptotic directions, and acceptance cones in the real geomagnetic field taking into account higher harmonics Cosmic ray latitude-longitude surveys on ships, trains, tracks, planes, balloons and satellites for determining the planetary distribution of the intensity of cosmic rays and how it changes with time Geomagnetic time variations of cosmic rays caused by the changing of internal sources of Earths main magnetic field and variable magnetospheric current systems Magnetospheric models and how to check them by galactic and solar cosmic rays The behaviour of cosmic rays in the atmospheres and magnetospheres of Venus, Mars, and Jupiter. The work concludes with a discussion of future developments and unsolved problems and contains a list of about thousand full references. This book will be of great interest to experts and students in cosmic ray research, solar-terrestrial physics, magnetosphere physics, and spacephysics.