In this talk, we will motivate and introduce the Langlands correspondence (in vague terms). We will begin by defining Hasse-Weil L-functions from a point-counting perspective, before seeing how we can think of them as arising from Galois representations. To see how these constructions might be related to automorphic representations, we will begin by considering the relationship between elliptic curves and cuspidal Hecke eigenforms described by the modularity theorem. We will then think about how to define L-functions for automorphic representations more generally, and how they may relate to Hasse-Weil L-functions. Finally, we will use Langlands’ formalism around L-functions of automorphic representations to think about a relationship between automorphic representations of different groups, as formulated in the functoriality conjecture.