This book is an introductory textbook on the physical processes occurring in the Earth's radiation belts. The presentation is at the advanced undergraduate or first year graduate level, and it is appropriate for students who intend to work in some aspect of magnetospheric physics. The treatment is quantitative and provides the mathematical basis for original work in this subject. The equations describing the motion of energetic ions and electrons in the geomagnetic field are derived from basic principles, and concepts such as magnetic field representations, guiding centre motion, adiabatic invariance, and particle distribution functions are presented in a detailed and accessible manner. Relevant experimental techniques are reviewed and a summary is given of the intensity and energy spectra of the particle populations in the Earth's radiation belts. Problem sets are included as well as appendices of tables, graphs and frequently used formulas.