What is the best way to learn Differential forms?

Solution 1:

The advice given elsewhere for doing math homework would seem (to me) too apply here as well. .. Namely, step 1) write down the problem. Step 2) cry.

That being said, differential forms probably aren't any more difficult than any other topics in mathematics (with the possible exception of tensors; which as I recall are closely related)...

Spivak's Comprehensive introduction to differential geometry is one source I remember. ..

Or maybe try guilleman and pollack's differential topology, or even Marsden and tromba's vector calculus has a section on them, I think...

Solution 2:

You should try this one: A visual introduction to Differential Forms - Fortney.

It's a nice book to see the geometric idea behind forms but without lost the formal formulation.