cover -- title page -- copyright page -- Acknowledgments -- Preface -- Contents -- Overview -- What is a group? -- A famous toy -- Considering the cube -- The study of symmetry -- Rules of a group -- Exercises -- What do groups look like? -- Mapmaking -- A not-so-famous toy -- Mapping a group -- Cayley diagrams -- A touch more abstract -- Exercises -- Why study groups? -- Groups of symmetries -- Groups of actions -- Groups everywhere -- Exercises -- Algebra at last -- Where have all the actions gone? -- Combine, combine, combine -- Multiplication tables -- The classic definition -- Exercises -- Five families -- Cyclic groups -- Abelian groups -- Dihedral groups -- Symmetric and alternating groups -- Exercises -- Subgroups -- What multiplication tables say about Cayley diagrams -- Seeing subgroups -- Revealing subgroups -- Cosets -- Lagrange's theorem -- Exercises -- Products and quotients -- The direct product -- Semidirect products -- Normal subgroups and quotients -- Normalizers -- Conjugacy -- Exercises -- The power of homomorphisms -- Embeddings and quotient maps -- The Fundamental Homomorphism Theorem -- Modular arithmetic -- Direct products and relatively prime numbers -- The Fundamental Theorem of Abelian Groups -- Semidirect products revisited -- Exercises -- Sylow theory -- Group actions -- Approaching Sylow: Cauchy's Theorem -- p-groups -- Sylow Theorems -- Exercises -- Galois theory -- The big question -- More big questions -- Visualizing field extensions -- Irreducible polynomials -- Galois groups -- The heart of Galois theory -- Unsolvability -- Exercises -- Answers to selected Exercises -- Bibliography -- Index of Symbols Used -- Index -- About the Author.