There are nine and sixty ways of constructing tribal lays-(Rudyard Kipling, "Ballads and Barrack Room Ballads")Virtually all of the "lays" of renormalizable quantum field theory can be found in Quantum Field Theory and Critical Phenomena. This remarkable work contains the most exhaustive collection of techniques, descriptions of subtleties and pitfalls, and helpful hints on the subject to date. Although several books have been written on critical phenomena-perhaps more of them on renormalizable field theories-yet none reaches the breadth or depth of the present book.The birth of quantum field theory nearly 50 years ago out of the divergences of quantum electrodynamics, and the emergence of the theory of universal properties of critical phenomena some 20 years ago, are only the beginnings of a very fertile intellectual enterprise. The author has participated in a large number of developments himself, and this book is a wonderful monograph conveying these subjects. The book is so clearly written and complete that students with a basic knowledge of quantum field theory can understand it. When they finish reading the book, they will be experts on the subject.The 40 chapters in this book are equally divided in four ways: (1) general renormalizable field theory; (2) particle physics applications and subtleties; (3) all about critical phenomena; and (4) instantons, mostly (not entirely) applied to the Bore1 summability of large-order perturbation series. At the end of each chapter are numerous relevant appendices, as well as textbooklike exercises for the reader. And yet, the book is not a textbook; rather, it is an encyclopedia written as a textbook.In an age where scientific results are published piecemeal and distributed in several journals and short review articles, it is gratifying to find a monograph that harks back to older times, when the material could all be found between the covers of a single book. I am confident that this book will find a place as a valuable sourcebook.PRADEEP KUMAR

We review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related O(n) matrix models.For d < 1 matter, the matrix problem can be completely solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively, in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representations of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising-like matter, the sum over topologies is reduced to the solution of non-linear differential equations (the Painlevé equation in the pure gravity case) which can be shown to follow from an action principle. In the case of pure gravity and more generally all unitary models, the perturbation theory is not Borel summable and therefore alone does not define a unique solution. In the non-Borel summable case, the matrix model does not define the sum over topologies beyond perturbation theory. We also review the computation of correlation functions directly in the continuum formulation of matter coupled to 2D gravity, and compare with the matrix model results. Finally, we review the relation between matrix models and topological gravity, and as well the relation to intersection theory of the moduli space of punctured Riemann surfaces. 6/93, submitted to Physics Reports Contents

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields φ and φ 2 ) of the 3D φ 4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N -vector