This book grew out of a graduate course on equilibrium states in ergodic theory which I gave twice (in winter 1994/95 and 1996/97) at the University of Erlangen. The text, as it is now, covers rather exactly 32 lectures of 90 minutes each plus a number of exercises. As my intention was (and still is) to put no more into this book than I was able to teach in such a one semester course, the material which I finally included strongly reflects my personal view of the field and is limited in both breadth and depth. But where the knowledgeable reader may wonder why certain topics are omitted or treated only under restrictive assumptions, the student who reads this book will hopefully profit from the concentration on key concepts and key examples gained in this way.

My goal in writing this book was to provide an introduction to the ergodic theory of equilibrium states which gives equal weight to two of its most important applications, namely to equilibrium statistical mechanics and to (time discrete) dynamical systems. In selecting the material, I always kept in mind some of the prime examples of these two fields: the two-dimensional Ising model, piecewise differentiable maps of an interval, and conformal iterated function systems. After working through the book, the reader not only has a solid basic knowledge of the general theory of equilibrium states, but has also seen applications of the theory to such different concepts as phase transitions, observable measures, and the dimension of fractals.