• Instructor's Preface
• Dependence Chart
• Student's Preface

1. Sets and Relations

1. Binary Operations
2. Groups
3. Abelian Groups
4. Nonabelian Examples
5. Subgroups
6. Cyclic Groups
7. Generating Sets and Cayley Digraphs

1. Groups and Permutations
2. Finitely Generated Abelian Groups
3. Cosets and the Theorem of Lagrange
4. Plane Isometries

1. Factor Groups
2. Factor-Group Computations and Simple Groups
3. Groups Actions on a Set
4. Applications of G -Sets to Counting

1. Isomorphism Theorems
2. Sylow Theorems
3. Series of Groups
4. Free Abelian Groups
5. Free Groups
6. Group Presentations

1. Rings and Fields
2. Integral Domains
3. Fermat's and Euler's Theorems
4. Encryption

1. The Field of Quotients of an Integral Domain
2. Rings and Polynomials
3. Factorization of Polynomials over Fields
4. Algebraic Coding Theory
5. Homomorphisms and Factor Rings
6. Prime and Maximal Ideals
7. Noncommutative Examples

1. Vector Spaces
2. Unique Factorization Domains
3. Euclidean Domains
4. Number Theory
5. Algebraic Geometry
6. Gröbner Basis for Ideals

1. Introduction to Extension Fields
2. Algebraic Extensions
3. Geometric Constructions
4. Finite Fields

1. Introduction to Galois Theory
2. Splitting Fields
3. Separable Extensions
4. Galois Theory
5. Illustrations of Galois Theory
6. Cyclotomic Extensions
7. Insolvability of the Quintic

A clear, in-depth introduction to abstract algebra 

• A focus on groups, rings and fields gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
  
• A study of group theory at the start of the text provides students with an easy transition to axiomatic mathematics.
  
• NEW / UPDATED - Many exercises in the text have been updated, and many are new. Most exercise sets are broken down into parts consisting of computations, concepts, and theory.
  
• • NEW - In response to feedback, answers to parts a), c), e), g), and i) of the 10-part true—false exercises are provided.
    
• Unsurpassed clarity of exposition:
  
• • Gives clear and concise explanations of the theory, with well-thought-out examples to highlight key points and clarify more difficult concepts.
    
  • Maintains the standard users expect from Fraleigh, while enhancing the clarity in a few sections. For example, sections in Part IX on Galois Theory have been rewritten to improve readability.
    
  • REVISED - Some topics have been reordered to streamline the flow of the book.
    
• A variety of high-quality exercises:
  
• • Numerous exercises in almost every section range from routine to very challenging. Exercises are computational, true/false, summarizing proofs, identifying errors, and proving statements.
    
  • REVISED - The 8th Edition replaces some exercises, re-words some, and adds other exercises.
    
• NEW - Applied topics — such as RSA encryption and coding theory as well as examples of applying Gröbner bases — have been added to the 8th Edition.
  
• Historical notes written by Victor Katz, an authority on the history of math, provide valuable perspective.

Check out the preface for a complete list of features and what's new in this edition.

• Many exercises in the text have been updated, and many are new. Most exercise sets are broken down into parts consisting of computations, concepts, and theory.
  
• • In response to feedback, answers to parts a), c), e), g), and i) of the 10-part true—false exercises are provided. 
• An Instructor Solutions Manual is available online at www.pearson.com to instructors only. Solutions to exercises involving proofs are sketches or hints which would not be in the proper form to turn in.
• Applied topics – such as RSA encryption and coding theory as well as examples of applying Gröbner bases – have been added to the 8th Edition.
• Some topics have been reordered to streamline the flow of the book.