TITLE: Good problem book in differential geometry
QUESTION [17 upvotes]: What are the books in Differential Geometry with a good collection of problems? At present I am having John M. Lee's Riemannian Manifolds, Kobayashi & Nomizu's Foundations of Differential 
Geometry. I particularly like Dieudonne's books in Analysis as well as books like Alexander Kirillov's Functional Analysis. To be precise, the books that have a huge number of exercises. The books  I mentioned are definitely not of that category. Can anyone please suggest differential geometry books that gives a lot of exercises?

REPLY [5 votes]: Andrew Pressley's Elementary Differential Geometry. This book is a very good book for beginners. It has quite an amount of exercises and with answers from within the book.