The aim of this winter school is to bring together researchers and students interested in the study of exceptional structures in geometry and physics. Historically fruitful examples of exceptional algebraic structures have included the E-series of simple Lie algebras, the Leech lattice, and the monster simple group. The discovery of each of these has led to new understanding of representation theory and the structure of fundamental physics, such as orbifold conformal field theory. We will focus on new efforts at classification, including recent work on fusion categories and hyperbolic Lie algebras, and on specific structures, such as the conjectural Mathieu symmetry underlying superconformal field theories attached to K3 surfaces. There is funding available, provided by the University of Tsukuba "Program to disseminate the Tenure Tracking System". Please request funding when registering.