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.

Preface

Chapter 1 symmetries of the tetrahedron

Chapter 2 axioms

Chapter 3 numbers

Chapter 4 dihedral groups

Chapter 5 subgroups and generators

Chapter 6 permutations

Chapter 7 isomorphisms

Chapter 8 plato's solids and cayley's theorem

Chapter 9 matrix groups

Chapter 10 products

Chapter 11 lagrange's theorem

Chapter 12 partitions

Chapter 13 cauehy's theorem

Chapter 14 coujugacy

Chapter 15 quotient groups

Chapter 16 homomorphisms

Chapter 17 actions, orbits, and stabilizers

Chapter 18 counting orbits

Chapter 19 finite rotation groups

Chapter 20 the sylow theorems

Chapter 21 finitely generated abelian groups

Chapter 22 row and column operations

Chapter 23 automorphisms

Chapter 24 the euclidean group

Chapter 25 lattices and point groups

Chapter 26 wallpaper patterns

Chapter 27 free groups and presentations

Chapter 28 trees and the nielsen-schreier theorem

Bibliography

Index