Recent progress in physics of disordered metals and semiconductors has led to the development of theoretical methods adequate for their description. Now, it is completely clear that such disciplines of theoretical physics as theories of disorder and quantum chaos are necessary to describe, for example, modern mesoscopic quantum devices. Moreover, these disciplines are converging toward each other, an exciting theoretical development. Although a lot of information can be obtained from numerical simulations, an analytical approach unifying disorder and chaos is definitely desirable. Besides, numerical simulation is often not conclusive and one has to have an analytical tool for calculations.

Currently the most efficient analytical method enabling us to achieve both goals is the supersymmetry technique, and many problems of disorder and chaos can be studied with a supermatrix nonlinear σ-model. The number of publications using the supersymmetry technique has been growing fast in the last 2–3 years. At the same time, many people still have a hesitation to start study of the method. The main reason is that they are afraid that manipulating the Grassmann anticommuting variables is something very difficult and, what is more important, that having spent a considerable time learning the technique, they would be able only to reproduce results that could be obtained by other more standard techniques. Such an attitude is to a great extent due to absence of a self-contained literature on the subject.