I am currently working through Spivak's Calculus and after want to properly learn vector calculus on my own. I don't want just to learn how to compute a gradient from some plug'n'chug book, but what manifolds, differential forms, exterior algebras, line, contour and multiple integrals and the rest are. I've been curious about all of that a while now and from what I understand that falls a bit within the purview of differential geometry and not strictly vector calculus.
What resources would you suggest for this, anons? A bit of googling has produced pic related as a potential textbook, would it be a suitable book for learning the stuff I've mentioned? Any other books or online resources you guys could recommend? I don't want just a wall of formulas and definitions; as this is essentially a geometric subject about Euclidean space, I would hope the text could appeal to my visual imagination/thinking as much as possible, wouldn't that be important in this subject?