I noticed this question posted on MO, hence I estimated that this may be an acceptable question even in MO (and not for MSE). I studied the notion of current and in a nutshell I understood "varifolds are weaker objects than currents."

My question is what kind of prerequisites one needs to have in order to study varifold theory and varifold geometry. For example, as far as currents are concerned, one needs to have grasped the notions of geometric measure theory and a bit of multilinear algebra and the introduction to distribution theory in functional analysis. I would like to ask the principal prerequisites one needs to know to fully grasp varifold theory. Geometric measure theory, of course, but how much Riemannian geometry? How much partial differential equation theory for the theory of regularity as well? Thank you very much in advance!