Explore the intricacies of quiver moduli spaces in this comprehensive lecture by Markus Reineke from Bochum. Delve into the algebraic varieties that encode continuous parameters of linear algebra type classification problems. Discover the recent developments in exploring the topological and geometric properties of quiver moduli spaces, and their applications to Donaldson-Thomas and Gromov-Witten theory. Gain insights into the motivation behind studying quiver moduli spaces from a representation theory perspective, and review their construction using Geometric Invariant Theory. Examine various classes of examples and explore results on the topology and geometry of these moduli spaces, with a particular focus on their cohomology. Conclude by investigating the applications of quiver moduli spaces to Gromov-Witten and Donaldson-Thomas theory through the lens of wall-crossing.