In this thesis we present Dijkgraaf-Witten theory. We start by considering a two-dimensional topological quantum field theory that can be used to prove Mednykh's formula along the way. Subsequently...Show moreIn this thesis we present Dijkgraaf-Witten theory. We start by considering a two-dimensional topological quantum field theory that can be used to prove Mednykh's formula along the way. Subsequently, we define the Dijkgraaf-Witten invariant as a partition function where we assign a specified weight to the 3-simplices of a compact, oriented and triangulated 3-manifold with boundary. The partition function depends on how we assign elements of a finite, discrete group G to all the oriented edges of the manifold. We prove that, whenever the triangulation of the boundary is fixed, the invariant does not depend on the triangulation of the manifold. Finally, we define a similar invariant where we model the weight of the 3-simplices to mimic the action of Chern-Simons theory. We demonstrate that by demanding invariance, we obtain the Dijkgraaf-Witten invariant.Show less