Preface
 Etymology
 Special Notation
 Chapter 1 Things Past
  1.1. Some Number Theory
  1.2. Roots of Unity
  1.3. Some Set Theory
 Chapter 2 Groups Ⅰ
  2.1. Introduction
  2.2. Permutations
  2.3. Groups
  2.4. Lagrange's Theorem
  2.5. Homomorphisms
  2.6. Quotient Groups
  2.7. Group Actions
 Chapter 3 Commutative Rings Ⅰ
  3.1. Introduction
  3.2. First Properties
  3.3. Polynomials
  3.4. Greatest Common Divisors
  3.5. Homomorphisms
  3.6. Euclidean Rings
  3.7. Linear Algebra
   Vector Spaces
   Linear Transformations
  3.8. Quotient Rings and Finite Fields
 Chapter 4 Fields
  4.1，Insolvability of the Quintic
   Formulas and Solvability by Radicals
   Translation into Group Theory
  4.2. Fundamental Theorem of Galois Theory
 Chapter 5 Groups Ⅱ
  5.1. Finite Abelian Groups
   Direct Sums
   Basis Theorem
   Fundamental Theorem
  5.2. The Sylow Theorems
  5.3. The Jordan-Holder Theorem
  5.4. Projective Unimodular Groups
  5.5. Presentations
  5.6. The Neilsen-Schreier Theorem
 Chapter 6 Commutative Rings Ⅱ
  6.1. Prime Ideals and Maximal Ideals
  6.2. Unique Factorization Domains
  6.3. Noetherian Rings
  6.4. Applications of Zom's Lemma
  6.5. Varieties
  6.6. Grobner Bases
   Generalized Division Algorithm
   Buchberger's Algorithm
 Chapter 7 Modules and Categories
  7.1. Modules
  7.2. Categories
  7.3. Functors
  7.4. Free Modules, Projectives, and Injectives
  7.5. Grothendieck Groups
  7.6. Limits
 Chapter 8 Algebras
  8.1. Noncommutative Rings
  8.2. Chain Conditions
  8.3. Serrusimple Rings
  8.4. Tensor Products
  8.5. Characters
  8.6. Theorems of Burnside and of Froberous
 Chapter 9 Advanced Linear Algebra
  9.1. Modules over PIDs
  9.2. Rational Canonical Forms
  9.3. Jordan Canonical Forms
  9.4. Smith Normal Forms
  9.5. Bilinear Forms
  9.6. Graded Algebras
  9.7. Division Algebras
  9.8. Exterior Algebra
  9.9. Determinants
  9.10. Lie Algebras
 Chapter 10 Homology
  10.1. Introduction
  10.2. Semidirect Products
  10.3. General Extensions and Cohomology
  10.4. Homology Functors
  10.5. Derived Functors
  10.6. Ext and Tor
  10.7. Cohomology of Groups
  10.8. Crossed Products
  10.9. Introduction to Spectral Sequences
 Chapter 11 Commutative Rings Ⅲ
  11.1. Local and Global
  11.2. Dedekind Rings
  Integrality
   Nullstellensatz Redux
   Algebraic Integers
   Characterizations of Dedekind Rings
   Finitely Generated Modules over Dedekind Rings
  11.3. Global Dimension
  11.4. Regular Local Rings
 Appendix The Axiom of Choice and Zorn's Lemma
 Bibliography
 Index