abstract: In this lecture, we outline the functional framework relevant for calculus of variations with differential forms. In this context, appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity are introduced. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem. It is a joint work with Bernard Dacorogna and Swarnendu Sil.