Finite group theory is a topic remarkable for the simplicity of its statements and the difficulty of their proofs. It is used in an essential way in several branches of mathematics - for instance, in number theory. This book gives an introduction to the subject; it is meant for graduate students, and for mathematicians interested in the connection between group theory and other mathematical topics. There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subgroups of GLn, and Small Groups. Each chapter is followed by a series of exercises. The present edition incorporates the correction of numerous errors found in the first revised edition of 2016. The author and publisher are grateful to Professor Bjorn Poonen of M.I.

T. and his associates, and to J. Sangroniz, for detecting and noting them.