The central aim of HIERATIC is to develop a new framework for understanding complex systems as a multi-level hierarchy of sub-systems using non-linear decompositions.To achieve this goal, HIERATIC is structured in three interlinked sets of activities: theoretical work, deriving the novel mathematics required to identify suitable non-linear state space reductions of complex systems; software development of efficient multi-scale simulation and prediction libraries; demonstrators, illustrating the power of our results – network dynamics, cell cycle simulations, social interactions in animals.The theoretical work will use unconventional approaches from topology and dynamical systems theory to derive an algorithmic approach to identifying "coarse-grainings" of large complex systems. These algorithms will be used to develop highly efficient simulation and prediction tools, integrated with the world-leading software libraries MASON and PRISM. The demonstrators will show the potential application of these techniques, in a range of applications, including validation on large empirical data sets.The project brings together leading researchers in complex systems theory, biosystems, multi-agent simulation, and experimental ecology, from around the EU and USA.