TITLE: Differential-geometry textbook with solved problems
QUESTION [5 upvotes]: I'm looking for a textbook in differential geometry which inside has exercises with (at least) final answers.
Since it's my first course in differential geometry it doesn't have to cover material (we finished the course with gauss-bonnet theorem)but rather to have hard-leveled problems. What book would you recommend to me ?

REPLY [6 votes]: 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.