This is a book intended for everyone interested in one of the most exciting and ambitious current developments in the field of physics and complex systems. A little bit of mathematics background may be helpful in certain sections of the book, but large parts can be read without any special prerequisites.

First we describe, in Chapters 1 and 2, what is meant by the notion self-organized criticality (SOC). We also list the characteristics of this behavior. In Chapter 3 we discuss a variety of systems that might exhibit the kind of behavior denoted by SOC. We discuss such systems as sandpiles, superconductors, earthquakes, and biological evolution. In Chapter 4 we describe various computer models of SOC. Most of these models are so simple that anyone with a PC can start right away to do numerical experiments on the models. Chapter 5 contains some mathematics. This chapter is dedicated to a discussion of different mathematical formalisms developed in order to understand the behavior of the computer models and so perhaps supply a mathematical description of real systems. Chapter 6 contains an attempt to assess to what extent the dream has come true – is, in fact, SOC ubiquitous? Several computer codes are included as appendices.

It is hoped that this will help the interested reader to start out on the path of numerical experiments. Some mathematical details are likewise deferred to the appendices. I believe the book can be read in at least three different ways. Those who are interested only in the overall “philosophical” impact of the ideas behind SOC can read Chapters 1, 2, and 6 for a start.