In this basic talk I will introduce exterior algebras and differential forms and motivate them as the natural objects carrying the information of oriented volume elements. I will discuss the de Rham complex and we’ll see some simple examples of how differential forms “know” about topology. In the end we’ll also talk about currents, which are a nice generalisation of differential forms, designed to incorporate forms with singularities as well as the natural duals to forms, namely – submanifolds.