Section 0. Sets and Induction
Section 1. Binary Operations
Section 2. Groups
Section 3. Fundamental Theorems about Groups
Section 4. Powers of an Element; Cyclic Groups
Section 5. Subgroups
Section 6. Direct Products
Section 7. Functions
Section 8. Symmetric Groups
Section 9. Equivalence Relations; Cosets
Section 10. Counting the Elements of a Finite Group
Section 11. Normal Subgroups
Section 12. Homomorphisms
Section 13. Homomorphisms and Normal Subgroups
Section 14. Direct Products and Finite Abelian Groups
Section 15. Sylow Theorems
Section 16. Rings
Section 17. Subrings, Ideals, and Quotient Rings
Section 18. Ring Homomorphisms
Section 19. Polynomials
Section 20. From Polynomials to Fields
Section 21. Unique Factorization Domains
Section 22. Extensions of Fields
Section 23. Constructions with Straightedge and Compass
Section 24. Normal and Separable Extensions
Section 25. Galois Theory
Section 26. Solvability