This monograph describes the behavior of cosmic rays (CR), mostly 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 Earth’s Magnetosphere Physics (CR may be shown using different magnetospheric models), and practically (CR determines a significant part of space weather effects on satellites and aircraft).The book contains eight chapters, dealing with the history of the discovery of CR geomagnetic effects and its importance for the determination of the nature of CR and energetically charged particles or gamma rays (Chapter 1); the first explanations of geomagnetic effects within the framework of dipole approximation of the Earth’s magnetic field (Chapter 2); trajectory computations of cutoff rigidities, transmittance functions, asymptotic directions, and acceptance cones in the real geomagnetic field with taking into account higher harmonics (Chapter 3); CR latitude-longitude surveys on ships, trains, tracks, planes, balloons and satellites for determining real CR intensity planetary distribution and how this changes with time (Chapters 4 and 5); geomagnetic time variations of CR caused by the changing of internal sources of Earth’s main magnetic field and variable magnetospheric current systems (Chapter 6); magnetospheric models and how to check them by galactic and solar CR (Chapter 7); behavior of CR in the atmospheres and magnetospheres of Venus, Mars, and Jupiter (Chapter 8). The work concludes with a list of about one thousand full references, a discussion on future developments and unsolved problems, as well as a subject index and an Appendix. This book will be of great interest to experts and students in CR research, Solar-Terrestrial Physics, Magnetosphere Physics, and Space Physics.