In 1965, when Professor Frank Ayres' Schaum's Outline of Modern Abstract Algebra was published, advanced algebra had undergone a number of significant developments on the abstract or theoretical plane, and the Schaum's Outline incorporated all the new elements, integrating them with the traditional material in the discipline. Since then this material has become a standard part of the curriculum, and the course in abstract algebra has developed its syllabus further. This new edition will supply a user-friendly, narrative introduction to the key ideas in abstract algebra, using the pedagogy of the Schaum solved-problem approach. Abstract algebra is an essential course in any undergraduate mathematics program, as well as necessary to many graduate students in mathematics. Abstract algebra treats the theoretical and conceptual topics in algebra, as distinct from the numerical questions that occupy students in lower level courses. The book will be organized into the four principal topics of abstract algebra: Sets and Relations; Number Systems; Groups, Rings, and Fields; and Linear Algebra. Major advances in theory have come particularly in the areas of groups and fields, all of which wi