The new science of complex systems will be at the heart of the future of the Worldwide Knowledge Society. It is providing radical new ways of understanding the physical, biological, ecological, and techno-social universe. Complex Systems are open, value-laden, multi-level, multi-component, reconfigurable systems of systems, situated in turbulent, unstable, and changing environments. They evolve, adapt and transform through internal and external dynamic interactions. They are the source of very difficult scientific challenges for observing, understanding, reconstructing and predicting their multi-scale dynamics. The challenges posed by the multi-scale modelling of both natural and artificial adaptive complex systems can only be met with radically new collective strategies for research and teaching.