Dummit and Foote Contents

PART I: GROUP THEORY.

• Chapter 1. Introduction to Groups.

• Chapter 2. Subgroups.

• Chapter 3. Quotient Group and Homomorphisms.

• Chapter 4. Group Actions.

• Chapter 5. Direct and Semidirect Products and Abelian Groups.

• Chapter 6. Further Topics in Group Theory.

PART II: RING THEORY.

• Chapter 7. Introduction to Rings.

• Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.

• Chapter 9. Polynomial Rings.

PART III: MODULES AND VECTOR SPACES.

• Chapter 10. Introduction to Module Theory.

• Chapter 11. Vector Spaces.

• Chapter 12. Modules over Principal Ideal Domains.

PART IV: FIELD THEORY AND GALOIS THEORY.

• Chapter 13. Field Theory.

• Chapter 14. Galois Theory.

PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA.

• Chapter 15. Commutative Rings and Algebraic Geometry.

• Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.

• Chapter 17. Introduction to Homological Algebra and Group Cohomology.

PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.

• Chapter 18. Representation Theory and Character Theory.

• Chapter 19. Examples and Applications of Character Theory.

• Appendix I: Cartesian Products and Zorn’s Lemma.

• Appendix II: Category Theory.