+lie Cartan's 1926-27 lectures on Riemannian geometry in an orthogonal frame were translated into Russian in book form in 1960. Now translated from Russian by Vladislav V. Goldberg, professor of mathematics at the New Jersey Institute of Technology and editor of the Russian edition, this book highlights Cartan's use of orthogonal frames to investigate the geometry of Riemannian manifolds and to solve problems in Euclidean and non-Euclidean spaces and in geodesics. The book introduces innovations such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature. Annotation c. Book News, Inc., Portland, OR (booknews.com)