This book is a basic introduction to the principles of circular particle accelerators and stage rings, for scientists, engineers and mathematicians. Based on the CERN accelerator school, it starts with a historical introduction to the field and an outline of the basic concepts of particle acceleration and focussing. It goes on to give more details of how the transverse and longitudinal motions of the particle beam can be analysed including treatments of lattice design, transition crossing, and other radio frequency effects. Operational and diagnostic techniques and the optimisation of luminosity are given appropriate emphasis. One chapter is devoted to radiation and the special features of synchrotron light sources. Although the book emphasizes circular accelerators, much of the treatment applies equally to linear machines and transfer lines. The book will be an essential reference to any one working with particle accelerators in the capacity of designer, operator or user, as well as for those intending to go to the frontiers of accelerator physics.