Includes index.

Definitions and examples of groups -- Subgroups and cosets -- Homomorphisms -- Group actions -- The sylow theorems and p-groups -- Permutation groups -- New groups from old -- Solvable and nilpotent groups -- Transfer -- Operator groups and unique decompositions -- Module theory without rings -- Rigns, ideals, and modules -- Simple modules and primitive rings -- Artinian rings and projective modules -- An introduction to character theory -- Polynomial rings, PIDs, and UFDs -- Field extensions -- Galois theory -- Separability and inseparability - -

Cyclotomy and geometric constructions -- Finite fields -- Roots, radicals, and real numbers -- Norms, traces, and discriminants -- Transcendental extensions -- The Artin-Schreier theorem -- Ideal theory -- Noetherian rings -- Integrality -- Dedekind domains -- Algebraic sets and the Nullstellensatz .