This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called ""geodesic ghor algebras"", a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of...