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If you want an "intuitive" approach, you might check out this new book: https://www.amazon.com/Visual-Differential-Geometry-Forms-Ma....

Disclaimer: I haven't read it (but I have heard good things).



I have read (part of) it, and it is excellent. I highly recommend it (alongside Needham’s VCA book).

But the lessons learned from there are largely orthogonal to the lessons you will learn from working with GA for a while.

To the grandparent, I would also recommend the very pretty book http://matrixeditions.com/5thUnifiedApproach.html




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