This book, based on a graduate course on Riemannian geometry and analysis on manifolds, given in Paris, covers the topics of differential manifolds, Riemannian metrics connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. This book addresses both the graduate student wanting to learn Riemannian geometry, and also the professional mathematician from a neighbouring field who needs information about ideas and techniques which are now pervading many parts of mathematics.
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