Sorry, I'm not sure if this question is 100% appropriate here; but I've tagged it as a soft question at least.
My goal is to finally learn what the differential symbols $dx$, or $f(x) dx$ actually mean. I know they are called "differential forms", and I have seen this term in chapter $5$ of Spivak's "Calculus on Manifolds", and the chapter is titled "Integration on Manifolds". However, the chapter before this is "Integration on Chains". I don't yet know what chains or manifolds are. Do I need to do that before doing chapter $5$?