This chapter is devoted to presenting some basic results concerning the differential structure on an arbitrary metric space. By a metric measure space, we mean a complete and separable metric space equipped with a non-zero non-negative Borel measure which is finite on bounded sets. In the literature, there are several possible definitions of Sobolev spaces in this setting, most prominently via p-upper gradients, p-relaxed slopes, and via test plans. Under minimal assumptions, all these definitions agree; we present these equivalent approaches in Appendix B and now introduce the most suitable definition for our purposes: the Newtonian space. We also present the definition of functions of bounded variation, their main properties, and discuss how to define the boundary measure of a set of finite perimeter and the relationships between them. In the second half of this chapter, we present the theory of Lp-normed modules and the first-order differential structure on metric measure spaces introduced by Gigli. We also recall the definition of divergence in the metric setting and discuss how to adapt these notions to the case of a sufficiently regular open subset of a metric measure space.