Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov–Tsankov–Videv theory.Contents:The Geometry of the Riemann Curvature TensorCurvature Homogeneous Generalized Plane Wave ManifoldsOther Pseudo-Riemannian ManifoldsThe Curvature TensorComplex Osserman Algebraic Curvature TensorsStanilov-Tsankov TheoryReadership: Researchers in differential geometry and mathematical physics.