The authors have used forty years of classroom experience to design a text that serves as a superb introduction to abstract algebra. All students, even those with no previous knowledge of abstract or linear algebra, will benefit from the Fifth Edition's organization and selection of topics. Outstanding features include: (1) builds abstraction on a solid foundation of concrete examples; (2) develops concepts gradually but allows for more rapid progress as students' mathematical maturity increases; (3) offers unparalleled problem sets; and (4) foreshadows important topics and then clearly presents and applies them to facilitate retention, not mere exposure. The historical and biographical notes on major contributors to the development of algebra show that mathematics continues to be created by real people. The preface shows how to use the text's flexibility to achieve any of several goals.