The success in the standard model and to the continuing research for a better understanding of the quantum chromodynamics has resulted in a great interest in spin physics among high energy and nuclear physics. Advances in accelerator technology have also spurred renewed interest in accelerating and storing highly aligned spin particles in synchrotrons and storage rings. The development of polarized ion sources and polarized electron sources have seen remarkable progress. With these advances in ion sources, there is a growing interest in the acceleration and maintenence of this polarization.This book is intended to be used as a graduate/senior undergraduate textbook in accelerator physics and sciences. The subject deals with acceleration and storage of polarized beams in high energy synchrotrons. The material covers the equation of motion for polarized beams in synchrotrons, spin depolarizing resonances, practical methods used in overcoming spin resonances, effects of spin rotators -- called Siberian snakes -- on the polarization vector, snake resonances, Sokolov-Ternov radiative polarization of electrons, and design principles of spin rotators. Experimental results of many polarized beam experiments are compared with theoretical analyses.Each chapter is also followed by exercises, which are intended to reinforce the concepts discussed, to derive useful formulae for applications, and to provide an introduction to some published literatures related to the polarized beam dynamics.