Complexity Science focuses on systems of many interdependent components, showing Emergent behaviour at the system level, Self-organisation and/or Evolution. At Warwick we draw on aspects of these in existing fields, including mathematics from dynamical systems and chaos, statistical inference, physics of phase transitions, self-assembly in chemistry, network modelling in biology and neuroscience, interacting agent modelling in economics and computer science. We also look to apply scientific methods in new fields of opportunity, such as transport, health and social science applications where mass quantitative data is newly available in this information age.