The contents of this book have been utilized in two courses given by the author. The first was a one-semester course for seniors at the University of British Columbia; it was clear that good undergraduates were perfectly capable of handling elementary group theory and its application to simple quantum chemical problems. The examples chosen in that course were mainly from ligand field theory, but that subject has been treated frequently enough at the elementary level to justify its being entirely left out of this volume. The second course was directed at first-and second-year graduate students of physical chemistry at the University of Pennsylvania, for which the prerequisites were a previous or concurrent year of quantum chemistry. Portions of the material were also used in a "valence" course for nonphysical chemistry students at the University of Pennsylvania.