There are two aspects to this book, at least how I refer to it: an introduction to the ADM formalism, and numerical analysis of black hole physics.
As an introduction to the ADM formalism, it stands alone. Chapter 2 "The 3+1 decomposition of Einstein's equations" provides a very pedagogical introduction ranging from "How to foliate spacetime" to performing calculations. Maxwell's equations in 3+1 dimensions are used as a motivation. Then the notion of the Hamiltonian constraint and momentum constraints are introduced, with some intuition given.
Chapter 3 "Constructing Initial Data" discusses the York time-slicing (a.k.a. conformal transformations of the spatial metric) and how that affects the constraints --- the momentum constraint becomes messy, the Hamiltonian constraint becomes pretty. Mass, momentum, and angular momentum is discussed in light of the problems of coordinate independence.
I frequently refer this book to my friends who need to learn the ADM formalism, it is the best introduction to the subject. The numerical analysis is equally as delightful.
Beware, though, of minor typos (e.g. page 23, "The 3+1 decompostion[sic] of..."). The math appears to be correct, the reasoning justified. Just sparse spelling errors.
Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.