preface chapter i.preliminaries-groups and rings 1. introduction to groups 2. quotient groups and sylow subgroups 3. finite abelian groups and solvable groups 4. introduction to rings 5. factoring in f[x] chapter ii. field exteio 1. simple exteio 2. algebraic exteio 3. splitting fields and normal exteio chapter iii. the galois correspondence 1. the fundamental correspondence 2. the solvable correspondence chapter iv. applicatio 1. cotructibility 2. roots of unity 3. wedderburn's theorem 3. dirichlet's theorem and finite abelian groups appendix a - groups 1. group actio and the sylow theorems 2. free groups, generato and relatio appendix b - factoring in integral domai 1. euclidean domai and principal ideal domai 2. prime and irreducible elements 3. unique factorization domai appendix c - vector spaces 1. subspaces, linear independence and spanning 2. bases and dimeion bibliogr