Faithful to its title this is a book on gravity, concentrating almost exclusively on the practical approximation techniques for comparing observed data to predictions of various gravitational theories. The book is primarily dedicated to providing the reader with a rich and complete supply of thoroughly explained and easily accessible formalisms. The expressions are primarily power series expansions in terms of $v/c$, and $rs/r$, where $rs=2GM/c2$ is the Schwarzschild radius for some central mass $M$ ($rs$ for the sun is only about 1.5 km). Such a series provides the main tool for comparing gravitational observation to theory.

It is a practical and, excuse the pun, down-to-earth book. Thus, as the authors comment, the reader should not expect to find much more than a mention of black holes, cosmology, etc. In fact, there is little or no treatment of the deep questions and mathematical formalisms theoretical gravitational research has developed and explored related to differential geometry, bundle theory, singularity theorems, topology, differential topology, etc. Also, there is no significant discussion of the vast arena of interaction (or lack thereof) between quantum theory and general relativity. All of these are part of the very important theoretical work inspired by Einstein's suggestion that gravity is to be understood in terms of mathematical structures on spacetime models but are not directly relevant to the purposes of this book. Consequently, it is definitely a handbook for experimentalists and not a textbook on Einstein's general relativity. The reader will find only a minimal and very sketchy introduction to the local description of the differential geometry of spacetime of special and general relativity. Rather, as the authors say, this is intended to be a textbook on the practical tools and facts relating to gravitational observations in terms of series expansions of the metric. For these limited purposes, it should be successful as a learning tool.

The mathematical physics needed to study this book is essentially that associated with undergraduate mechanics, Newtonian gravity, and introductory special relativity. From there, the book presents a very limited and elementary discussion of differential geometry and its application to Einstein's general relativity. After presenting metric approximation tools, the book closes with summaries of various alternatives to Einstein theory and their current experimental standing. The general organization of this book is as follows.

The first part, three chapters, is on Newtonian gravity, and includes a basic formulation of the theory including a detailed study of the equations of motion of point particles and extended bodies, problems related to self-gravitating matter, and orbital dynamics. This last topic is treated extensively because solar system tests have been so important in testing gravity theories. There is also a discussion of the equivalence principle, and the tests by Eötvös and others, to an extent not common in other textbooks. Because Newtonian gravity was so successfully verified by observations until about a hundred years ago, it naturally forms the solid basis for the first order approximation to gravity. One of the authors, Will, has been a leading contributor to the development of PPN, “Parameterized Post Newtonian,” perhaps the most widely used power series tool for comparing gravitational observation to theory.

The next part begins the exploration of spacetime geometry in terms of the metric. Chapter 4 introduces the concept of 4D spacetime, the Minkowski metric, and both the kinematics and dynamics of special relativistic motion. Chapter 5 begins with problems inherent in extending Newtonian gravity to special relativity. It then proceeds via the equivalence principle to the suggestion that gravity could be described by some structure of spacetime, specifically geometric. With this motivation, the elementary mathematical tools for investigating its curvature are introduced. This is all done locally in terms of coordinates and no mention is made of modern bundle or gauge theory constructs. The Einstein equations are simply stated with only brief discussion of the motivations for them. The Schwarzschild solution, inner and outer form, is presented and thoroughly explored.

The next part is “Post Minkowskian.” Chapter 6 introduces the Landau and Lifshitz tensor densities approach, theoretically clumsy but practically very important for later approximations, including gravitational radiation. Chapter 7 “assembles the tools,” as the first section says. These are primarily iterative approximations to a very wide class of solutions to the Einstein equations in terms of the stress-energy tensor.

Chapters 8, 9, and 10 are “Post Newtonian,” involving expansions in terms of the dimensionless ratios $v/c$ and $rs/r$. These chapters are very detailed, and include reference to fairly recent results such as binary pulsars, time keeping, and the Schiff precession.

Chapters 11 and 12 deal with gravitational radiation up to and beyond the quadrupole terms in terms of both experimental observation of it and its production, such as with binary stars, and radiation energy loss.

Chapter 13 closes with a discussion of alternative theories, which includes at least mention of most of the recent and current ones. It is in this context that the important PPN notation and parameters are defined and studied.

Finally, it must be said that no book of reasonable length (*Gravity* is almost 800 pages) could be expected to cover all of the topics of current interest in general relativity, but certainly *Gravity* does an excellent job of fulfilling its limited express intent of presenting the practical techniques used for exploring consequences of various gravitational theories and observations. This is done in easily understood pedagogical form that includes a nice list of exercises for each chapter.

*Carl H. Brans is J. C. Carter Emeritus Professor of Theoretical Physics at Loyola University, New Orleans. His current research interests involve relating exotic differential structures to spacetime models.*