This is a paperback edition of a distinguished book, originally published by Clarendon Press in 1971. It was then the first text on critical phenomena, a field that has enjoyed great activity for the past twenty years and that still continues to attract much attention. The book is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another. (A simple example is the melting of a solid to become a liquid.) Such a transformation is termed 'critical' when, after a certain amount of the substance changes phase, the entire bulk virtually instantaneously also makes the transition. A second, updated edition is planned for future publication, but in the mean time this paperback reissue will be useful in teaching the fundamental principles of this extremely interesting subject.