This book is based on a short graduate course given by one of us () at New York University and at Bar-Ilan University, Israel. The decision to publish these lectures as a book was made, after some doubts, for the following reason. The theory of phase transitions, with excellent agreement between theory and experiment, was developed some forty years ago culminating in Wilson’s Nobel prize and the Wolf prize awarded to Kadanoff, Fisher and Wilson. In spite of this, new books on phase transitions appear each year, and each of them starts with the justification of the need for an additional book. Following this tradition we would like to.