# Looking for a good alternative to 'An introduction to manifolds' by Loring W. Tu

I'm currently studying some basic theory about manifolds from the book 'An introduction to manifolds' by Loring W. Tu.

The problem I have with this book is that there are very little exercises, and the exercises that are included are quite easy and do not really serve to provide you with any real insight by forcing you to think deeply about the material.

I do like the pace and assumed prerequisites of the book.

So I'm looking for something similar to this book but with more and harder/more interesting exercises.

Thanks.

• It's a little hard to say what a hard intro differential geometry exercise should be. In some sense you're setting up notation (a formidable amount, granted) for a few hundred pages. Have you looked at Guillemin-Pollack? That's a fun book. They do favor proving geometric theorems over building up the formalism (everything is in $\mathbb{R}^n$, for example) but you might like it. Combining it with Tu's book could be great. – Hoot Jul 18 '15 at 21:03
• @Hoot That might be a fair point. All theorems so far are basically just pretty straightforward substitutions of one definition into the next, so I can imagine that it's hard to come up with nice exercises. Still hope they exist though – user2520938 Jul 18 '15 at 21:05