Moduli spaces of representations associated to quivers are algebraic varieties encoding the continuous parameters of linear algebraic classification problems. In recent years their topological and geometric properties have been explored to investigate wild quiver classification problems.The goal of this talk is the construction of the Nakajima variety of a quiver as one of these moduli spaces. Starting with basic definitions from the representation theory of quivers, fundamental concepts like doubling and framing are introduced. Via geometric invariant theory Nakajima varieties can be defined. We will discuss their properties focusing on the example of the quiver consisting of one vertex and no arrows. Finally, further relations to recent research interests are explained.