Russian academics Novikov and Taimanov present the basics of Riemannian geometry in its modern form as the geometry of differentiable manifolds and the most important structures on them. Coverage includes the basics of various geometries in linear spaces, the geometry of two-dimensional manifolds, basics of topology of smooth manifolds, Lie groups, classical tensor algebra and tensor calculus, differential forms theory, the Riemannian theory of connections and curvature, conformal geometry, complex geometry, Morse theory and Hamiltonian formalism, Poisson and Lagrange manifolds, multidimensional variational problems, and geometric fields in physics. Assumes prior completion of several basic undergraduate courses, such as advanced calculus, linear algebra, ordinary differential equations, and elements of topology. Translated from Russian by Dmitry Chibisov. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)