Books about manifolds?

Question

I would like to learn about manifolds. Please can someone recommend me a good book to learn about manifolds?

Answer 1

I like

Introduction to Smooth Manifolds by John M. Lee.

The wikipedia article on manifolds is also quite nice and contains a number of references.

Answer 2

Detailed and well explainediscussion about manifolds can be seen in Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner.

Answer 3

A widely used and known reference is Kodayashi and Nomizu's Foundations of differential geometry. Another great one is Spivak's Comprehensive Introduction to Differential Geometry. I liked the style of Choquet-Bruhat and De Witt-Morette's Analysis, Manifolds and Physics: it contains examples from classical physics and more.

There are tons of other good books, but these three are the first ones that popped up into my mind :-)

Answer 4

I suggest you to have a complete look at

Elementary Differential Geometry by Barrett O'Neill

then

Differentiable Manifolds an Introduction by F Brickell & R. S. Clark.

However it is an old one, I had good times while taking a course studying it before. This is a good one. Also, if you are interested to have a $\color{red}{\text{c}}\color{blue}{\text{o}}\color{green}{\text{l}}\color{brown}{\text{o}}\color{yellow}{\text{r}}ful$ $\color{purple}{\text{nightmare}}$, you may see this complete reference:

A Comprehensive Introduction to Differential Geometry by M. Spivak.

Answer 5

Loring Tu's Introduction to manifolds is a very good book as has been mentioned already. 'An Introduction to Differentiable Manifolds and Riemannian Geometry' by W.Boothby is another book that you may like to consider.