This book describes methods for calculating magnetic resonance spectra which are observed in the presence of random processes. The emphasis is on the stochastic Liouville equation (SLE), developed mainly by Kubo and applied to magnetic resonance mostly by J H Freed and his co-workers. Following an introduction to the use of density matrices in magnetic resonance, a unified treatment of Bloch–Redfield relaxation theory and chemical exchange theory is presented. The SLE formalism is then developed and compared to the other relaxation theories. Methods for solving the SLE are explained in detail, and its application to a variety of problems in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) is studied. In addition, experimental aspects relevant to the applications are discussed. Mathematical background material is given in appendices.