The history of integrable systems goes back to 19th century work in classical mechanics, differential geometry, complex analysis, differential equations and nonlinear special functions. The modern theory is grew up around the study of KdV type equations, following the discovery of multi-soliton solutions, infinite number of conservation laws and the Inverse Scattering Transform in the 1960s and 1970s. In the 1980s new ideas came via integrable field theories and connections with harmonic maps and differential geometry were re-established. Links with other areas of mathematics - algebraic geometry, twistor theory, self-duality, representation theory, number theory, enumerative geometry, Gromov-Witten theory and Topological Quantum Field Theories grew in the 1990s and through into the 21st Century. The aim of the Symposium is to bring together leading international researchers in the various sub-fields of integrable systems, concentrating primarily on the mathematical aspects of the theory.