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by bmitc 2220 days ago
I listed references elsewhere.

https://news.ycombinator.com/item?id=23270163

Edwards' first three chapters give a wonderfullly intuitive exposition of forms and their application to integration.

Tu's book is a rigourous study of smooth manifolds and differential forms. His exercises are approachable, and his book is the most expedient to the full theory of differential forms.

As a quirky intuition pump, I recommend Geometrical Vectors by Gabriel Weinreich. The Fortney book mentioned in another comment is a nice, visual book, and there are other references in the replies to the comment I linked.