Joseph A. Gallian earned his PhD from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.

• 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 Rings 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 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