This set of notes grew out of a course that I gave at Ohio University in the spring of 1996. My aim was to give graduate students who were familiar with ordinary character theory an introduction to Brauer characters and blocks of finite groups.

To do that I chose an objective: the Glauberman Z*–theorem. This theorem gives an excellent excuse for introducing modular representation theory to students interested in groups. Glauberman's outstanding result is one of the major applications of the theory to finite groups. However, to be able to prove it, one needs to proceed from the very basic facts to the three main theorems of R. Brauer.

In Chapter 1, I prove what is absolutely necessary to get started. Assuming that the students have already had a course on ordinary characters, I use this chapter to remind them of some familiar ideas while introducing some new ones.

In Chapter 2, I introduce Brauer characters (in the same spirit as in the book of M. Isaacs) and develop their basic properties.

In Chapter 3, I introduce blocks and, in Chapter 4, Brauer's first main theorem is given. The second main theorem is proven in Chapter 5 and its proof is a new “elementary” proof by Isaacs based on work by A. Juhász and Y. Tsushima. The third main theorem is given in a very general form and its proof is due to T. Okuyama. Once the third main theorem has been proven, we are ready for the Z*–theorem.