Ian Anderson - "Symmetry reduction and Darboux Integrability". The method of Darboux is a technique for finding the general solution to scalar, second order partial differential equations in two independent variables. In this talk I will describe a far-reaching generalization of this classical method which allows one to explicitly solve more general systems of PDE. This new approach is based upon the idea of "inverse" symmetry reduction of differential systems. This approach exposes the fundamental geometric invariants for any Darboux integrablity system, allows for the algorithmic integration of such equations, and provides new insights in many geometrical aspects of Darboux integrability. For example, I will show how this theory allows one to easily construct examples of non-linear Laplace transformations.