2. Introduction to Groups.

3. Equivalence. Congruence. Divisibility.

4. Groups.

5. Group Homomorphisms.

6. Introduction to Rings.

7. The Familiar Number Systems.

8. Polynomials.

9. Quotient Rings.

10. Field Extensions.

11. Galois Theory.

12. Geometric Constructions.

13. Applications of Permutation Groups.

14. Symmetry.

15. Cryptography. Algebraic Coding.

16. Lattices and Boolean Algebras.

Appendix A: Sets.

Appendix B: Proofs.

Appendix C: Mathematical Induction.

Appendix D: Linear Algebra.

Appendix E: Solutions to Selected Problems.

Index.