Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Integers and Equivalence Relations -- 0. Preliminaries -- Groups -- 1. Introduction to Groups -- 2. Groups -- 3. Finite Groups -- Subgroups -- 4. Cyclic Groups -- 5. Permutation Groups -- 6. Isomorphisms -- 7. Cosets and Lagrange's Theorem -- 8. External Direct Products -- 9. Normal Subgroups and Factor Groups -- 10. Group Homomorphisms -- 11. Fundamental Theorem of Finite Abelian Groups -- 12. Introduction to Rings -- 13. Integral Domains -- 14. Ideals and Factor Rings -- 15. Ring Homomorphisms -- 16. Polynomial Rings -- 17. Factorization of Polynomials -- 18. Divisibility in Integral Domains -- Fields -- 19. Extension Fields -- 20. Algebraic Extensions -- 21. Finite Fields -- 22. Geometric Constructions -- Special Topics -- 23. Sylow Theorems -- 24. Finite Simple Groups -- 25. Generators and Relations -- 26. Symmetry Groups -- 27. Symmetry and Counting -- 28. Cayley Digraphs of Groups -- 29. Introduction to Algebraic Coding Theory -- 30. An Introduction to Galois Theory -- 31. Cyclotomic Extensions.