PART I: NONCOMMUTATIVE ALGEBRA 1. Definitions and Examples of Groups 2. Subgroups and Cosets 3. Homomorphisms 4. Group Actions 5. The Sylow Theorems and p-groups 6. Permutation Groups 7. New Groups from Old 8. Solvable and Nilpotent Groups 9. Transfer 10. Operator Groups and Unique Decompositions 11. Module Theory without Rings 12. Rings, Ideals, and Modules 13. Simple Modules and Primitive Rings 14. Artinian Rings and Projective Models 15. An Introduction to Character Theory PART II: COMMUTATIVE ALGEBRA 16. Polynomial Rings, PIDs, and UFDs 17. Field Extensions 18. Galois Theory 19. Separability and Inseparability 20. Cyclotomy and Geometric Constructions 21. Finite Fields 22. Roots, Radicals, and Real Numbers 23. Norms, Traces, and Discriminants 24. Transcendental Extensions 25. The Artin-Schreier Theorem 26. Ideal Theory 27. Noetherian Rings 28. Integrality 29. Dedekind Domains 30. Algebraic Sets and the Nullstellensatz Index