Introduction to Riemannian Manifolds (Second Edition)
by John M. Lee · Springer (Graduate Texts in Mathematics 176)
Graduate text, formerly titled Riemannian Manifolds: An Introduction to Curvature, covering connections, geodesics, the Riemann, Ricci and scalar curvature tensors, Jacobi fields, Gauss-Bonnet, and comparison theorems. Requires prior knowledge of smooth manifolds.
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