In this lecture I will talk about one of the most useful concepts to Theoretical Physics in Advanced Mathematics, discussing why so and what do they provide us with? I will talk about the p-forms in detail, introducing wedge products, exterior derivatives and corresponding anti-derivatives. In the end we talk about the basis of a p-form and then the physical significance of differential forms and their relation to topology, where I briefly talk about D-Branes in relation to String theory.