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Numbers measure size, groups measure symmetry. the first statement comes as no surprise; after all, that is what numbers are for. the second will be exploited here in an attempt to introduce the vocabulary and some of the highlights of elementary group theory. A word about content and style seems appropriate. in this volume, the emphasis is on examples throughout, with a weighting towards the symmetry groups of solids and patterns. almost all the topics have been chosen so as to show groups in their most natural role, acting on ��or permuting�� the members ora set, whether it be the diagonals of a cube, the edges of a tree, or even some collection of subgroups of the given group. the material is divided into twenty-eight short chapters, each of which introduces a new result or idea.a glance at the contents will show that most of the mainstays of a first course arc here. the theorems of lagrange, cauchy, and sylow all have a chapter to themselves, as do the classifcation of finitely generated abelian groups, the enumeration of the finite rotation groups ��and the plane crystallographic groups, and the nielsen-schreier theorem.