TITLE: Recommendations for differential geometry textbooks that develop geometric intuition.
QUESTION [7 upvotes]: I'm currently self-studying complex analysis (CA), and reading "Visual Complex Analysis" by Tristan Needham. I'm absolutely fascinated by how much geometric intuition he provides for the key findings in CA. It has been a very enticing read so far. 
I have a mechanical engineering background, I've previously self-studied general/algebraic topology, and I'm interested in self-studying differential geometry (DG) after finishing Needham's book. I know that Needham is in the process of releasing his next book, "Visual Differential Geometry". But the exact date of release is hard to find. Can anyone recommend a few good DG textbooks that (a) pay special attention to developing the geometric intuition of the reader (and perhaps less attention to rigorous mathematical proofs), and (b) would be appropriate for a reader with my aforementioned background?

REPLY [2 votes]: Although the book is to be available 14 July in the states, if you buy it directly from Princeton University Press, they'll ship it to you now.
I'm only through 55 of its 464 pages of text, and it's fabulous.  Tons of pictures.  The diagrams to explain the changes in the metric from the sphere to the complex plane are gems.
You cannot find a page with only text and no equations or pictures.
Buy it