Book recommendation for Introductory Differential Geometry, with lots of examples (calculations) Could you give a recommendation for differential geometry or curves and surfaces with lots of examples and calculations?
I need lots of examples to understand a topic therefore it would great if there are some book with good calculations.
 A: Barrett O'Neill's Elementary Differential Geometry. A classic, you can't go wrong with this one..
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A: The ones I used and liked were:
Differential Geometry of Curves and Surfaces - Manfredo Do Carmo
Modern Differential Geometry of Curves and Surfaces with Mathematica - Alfred Gray
A: For the geometry of surfaces I recommend the book Differential Geometry of Curves and Surfaces by Manfredo Do Carmo,  which is clear, self-contained and with a lot of examples and exercises.
If you want to go further and learn modern differential geometry (manifolds etc) an excellent book is An introduction to manifolds by Loring Tu, which contains a lot of examples and explicit calculations. Moreover it is self-contained, and has a lot of appendices in the case you have to strengthen you background.
Another very good book about manifolds is Introduction to smooth manifolds by Lee. You can read some of its chapters as a complement of Tu’s book, indeed it contains some important topics that you can’t find in the book of Loring Tu.
