This book is based on a first-year graduate course given regularly by the first author at the University of Chicago, most recently in the autumn quarters of 1991,1992,and 1993. The lectures given in this course were expanded and prepared for publication by the second author.
The aim of this book is to provide a concise yet thorough treatement of some topics from group theory and representation theory with which every mathematician should be well acquainted. Of course, the topics covered naturally reflect the viewpoints and interests of the authors; for instance, we make no mention of free froups, and the emphasis throughout is admittedly on finite groups. Our hope is that this book will enable graduate students from every mathematical field, as well as bright undergraduates with an interest in algebra, to solidify their knowledge of group theory.