Good problem book in differential geometry

This book (Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers) contains detailed solutions to 375 core exercises on differentiable manifolds, Lie groups, fiber bundles, and Riemannian geometry. It should be helpful to anyone who needs to aquire a solid working technique in these fields and to students who have problems to illustrate concepts, methods, and theorems by examples.


John M. Lee's Introduction to Smooth Manifolds is also a great book with lots of exercises.


Barrett O'Neill's book "Elementary Differential Geometry" is really good. He has tons of exercises and he's a mathematical physicists/ diff. geometer so there you go. He also has a text on black holes and another text called "Semi-Riemannian Geometry" (tons of physics applications, problems).

$\textbf{Update}$: Loring Tu also has a differential geometry book now.

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Riemannian Geometry

Differential Geometry

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