This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)�the study of
a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian
geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have
developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward
global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this
divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results
of compelling mathematical interest.