Preface ; Notations ; Preliminaries: Sets and Mappings ; Equivalence Relation ; The Integers ; The Axiom of Choice ; Countable and Uncountable Sets ; Groups: Definitions and Examples ; Subgroups ; Cosets and Normal Subgroups ; Homomorphisms ; Normalizer, Centralizer and Class Equation ; Symmetric Groups ; Direct Products ; Automorphisms ; Sylow's Theorems ; Applications of Sylow's Theorems ; Series of Groups ; Finite Abelian Groups ; Groups of Small Order ; Rings: Definitions and Examples ; Ideals and Isomorphism Theorems ; Direct Product of Rings ; Rings of Polynomials ; Fields of Fractions ; Prime Ideals and Maximal Ideals ; Factorization in Integral Domains ; Noetherian Rings ; Modules: Definitions and Examples ; Module Homomorphisms and Quotient Modules ; Direct Sums and Exact Sequences ; Free Modules ; Free Modules over PIDs ; Finitely Generated Modules over PIDs ; Projective and Injective Modules ; Semisimple Modules ; Fields: Field Extensions ; Splitting Fields ; Algebraically Closed Fields ; Normal Extensions ; Separable Extensions ; Galois Theory ; Galois Group of a Polynomial ; Radical Extensions ; Constructibility ; Bibliography ; Index.