Introduction.

Complexity, a century-old problem with seemingly endless possibilities, has driven scientists from all disciplines within Natural and Computing Sciences to test the limits of their paradigms and theories, eventually, bringing them together in the hope of creating a new paradigm that could shed light into the Complexity problems. One of the most intensely scrutinised problems in this emerging cross- and inter-disciplinary Science of Complexity, is to determine the mathematical principles and underlying mechanisms that give rise to the emergence of collective behaviour in complex systems, namely, systems that are composed by many interacting units or sub-systems (Fig. 1.1). Researchers across the world have turned their attention into finding the minimal set of variables and conditions that one needs to explain and predict these collective behaviour, which emerge without the need for any central control or external driving force, namely, they self-organise.