This book presents the basic theory and applications of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential. Some special features of this book are: exposition of the basic theory at a level to facilitate independent study; discussion of the various versions of the theory: diffusion Monte Carlo, Green’s function Monte Carlo, and release node Monte Carlo; and commentary on the important features that distinguish this stochasic approach from ab initio methods.