Table of Contents

The alternating groups.- The classical groups.- The exceptional groups.- The sporadic groups.

Reviews

From the reviews: "The book under review has as its main goal to give an introductory overview of the construction and main properties of all finite simple groups. ... This book is the first one that attempts to give a systematic treatment of all finite simple groups, using the more recent and efficient constructions ... . The author succeeds in making this important but difficult area of mathematics readily accessible to a large sector of the mathematical community, and for this we should be grateful." (Felipe Zaldivar, The Mathematical Association of America, March, 2010) "One of the great achievements of mathematics was the classification of the finite simple groups ... . the book brings much information to the classroom. It contains exactly those things one would like to know if one were to meet the individual simple groups for the first time. ... perfectly suitable for an advanced course or seminar. ... accessible also to those who are not great experts in group theory. Anyone interested in finite groups ... should have this book on his or her bookshelf." (Gernot Stroth, Mathematical Reviews, Issue 2011 e) "The author of this book has succeeded in giving an overview of all non-abelian finite simple groups which is accessible to non-experts. ... For anyone who wants to get information on finite simple groups without having to tackle massive monographs this volume will be most welcome." (Ch. Baxa, Monatshefte fur Mathematik, Vol. 164 (3), November, 2011) "It is the first text at this level in which all the finite simple groups are treated together, pointing out their connections. ... The text is very well organised. The introduction, which forms the first chapter, contains a brief history and the statement of the classification theorem, together with sections giving remarks on the applications and the proof of the theorem. ... Consequently the book may also be useful to a reader who just wants an introduction to a particular group or family of groups." (Peter Shiu, The Mathematical Gazette, Vol. 95 (532), March, 2011)