A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition

Based on my reading of vol 1 and my browsing of vol 2 of this series, there is no doubt that Michael Spivak and differential geometry are a delightful combination. So I ordered vol 3-5 as well. And I learned that 90% of these three volumes is about A) the imbedding of manifolds in manifolds and B) the extrinsic properties of the imbedded manifold relative to the containing manifold. This is to be contrasted with vol 1-2, which is 90% about the intrinsic properties of a manifold. I found vol 3-5 of little interest to me as a physicist and not particularly interesting to me as a mathematician. So I returned the 3 volumes and spent the money on Araki's book on algebraic quantum field theory.So, if imbedding manifolds does not excite you, I'm afraid that you should pass on these three volumes.

What can one say about Spivak's books on differential geometry. I used a complete set in my undergrad years and used them so much that I wanted a new copy! Definitely one set of books worth having in every mathematician's library.

Mr Spivak manages to slaughter a beautiful topic in math by being unable to explain the topic properly.Fortunately I've had better teachers in my training, as well as better books.

These are classics

Nothing

It's OK

Price too much.