A successful one-week short course on Complex Systems Beyond the Metaphor: Your Mathematical Toolset was held in the UNSW School of Mathematics and Statistics on Feb 5-9, 2007. It introduced the mathematical foundations and tools needed for a solid understanding of complex systems, an area often known for purely metaphorical or 'hand-waving' explanations. Aiming at a mathematically literate audience (e.g. engineers, quantitative biologists, computer modellers), leading Australian experts presented intensive introductions to the essential topics of complex systems theory, including self-organization, nonlinear dynamical systems, cellular automata, networks and statistical learning.