Differential and Riemannian Manifolds (Graduate Texts in Mathematics)
S. LangDifferential and Riemannian Manifolds"An introduction to differential geometry, starting from recalling differential calculus and going through all the basic topics such as manifolds, vector bundles, vector fields, the theorem of Frobenius, Riemannian metrics and curvature. Useful to the researcher wishing to learn about infinite-dimensional geometry."—MATHEMATICAL REVIEWS