A quiver Q is a finite, directed multi-graph. A quiver representation is an assignment of a finite dimensional vector space to each vertex of Q and a linear map to each directed edge. Gabriel’s theorem characterizes the quivers with finite representation type. That is, Gabriel’s theorem characterizes which quivers will have finitely many isomorphism classes of indecomposable representations. This seminar will be comprised of detailed definitions and examples of quivers and their representations along with a proof of one direction of Gabriel’s theorem using entry level algebraic geometry and will be accessible to all with knowledge of linear algebra, basic topology, and some group theory.