The classification of the finite simple groups is one of the major intellectual achievements of this century, but it remains almost completely unknown outside of the mathematics community. This introduction to group theory is also an attempt to make this important work better known. Emphasizing classification themes throughout, the book gives a clear and comprehensive introduction to groups and covers all topics likely to be encountered in an undergraduate course. Introductory chapters explain the concepts of group, subgroup and normal subgroup, and quotient group. The homomorphism and isomorphism theorems are explained, along with an introduction to G-sets. Subsequent chapters deal with finite abelian groups, the Jordan-Holder theorem, soluble groups, p-groups, and group extensions. The numerous worked examples and exercises in this excellent and self-contained introduction will also encourage undergraduates (and first year graduates) to further study.

1.Definitions and examples 2.maps and relations on sets 3.elementary consequences of the definitions 4.subgroups 5.cosets and lagrange's theorem 6.error-correcting codes 7.normal sobgroups and quotient groups 8.the homomorphism theorem 9.permutations 10.the orbit-stabiliser theorem 11.the sylow theorems 12.applications of sylow theory 13.direct products 14.the classification of finite abelian groups 15.the jordan-holder theorem 16.composition factors and chief factors 17.soluble groups 18.examples of soluble groups 19.semidirect products and wreath products 20.extensions 21.central and cyclic extensions 22.groups with at most 31 elements 23.the projective special linear groups 24.the mathieu groups 25.the classification of finite simple groups

John Humphreys is at University of Liverpool.

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