The classical Stokes’ Theorem is a familiar result from vector calculus, relating the integral over a surface inR3to the integral over the1-dimensional boundary of that surface. A series of other classical theorems offer similar relationships between the integral over a region and an integral over its boundary, including Green’s Theorem, the Divergence Theorem, and even the Fundamental Theorem of Calculus. The General Stokes’ Theorem extends this relationship to k-dimensional manifolds-with-boundary. In order to understand this generalization, we introduce the differential form as a new type of integrand. Differential forms offer a coordinate-free approach to vector calculus, which in turn will allow us to define integration over manifolds and ultimately to define the General Stokes’ Theorem. This talk should be accessible to students with a background in vector calculus and linear algebra.