This set of lecture notes is focused on the noncommutative aspects of the study of rings and modules. It is intended to complement the book Steps in Commutative Algebra, by R. Y. Sharp, which provides excellent coverage of the commutative theory. It is also intended to provide the necessary background for the book An Introduction to Noncommutative Noetherian Rings, by K. R. Goodearl and R. B. Warfield.

The core of the first three chapters is based on my lecture notes from the second semester of a graduate algebra sequence that I have taught at Northern Illinois University. I have added additional examples, in the hope of making the material accessible to advanced undergraduate students. To provide some variety in the examples, there is a short section on modules over the Weyl algebras. This section is marked with an asterisk, as it can be omitted without causing difficulties in the presentation. (The same is true of Section 1.5 and Section 3.4.) Chapter 4 provides an introduction to the representation theory of finite groups. Its goal is to lead the reader into an area in which there has been a very successful interaction between ring theory and group theory.

Certain books are most useful as a reference, while others are less encyclopedic in nature, but may be an easier place to learn the material for the first time. It is my hope that students will find these notes to be accessible, and a useful source from which to learn the basic material.