The study of Complex Systems refers to the emergence of collective properties in systems with a large number of parts in interaction among them. These elements can be atoms or macromolecules in a physical or biological context, or machines or companies in a socio-economic context.     

The science of complexity tries to discover the nature of the emerging behavior of Complex Systems, often invisible to the traditional approach, by focusing on the structure of the interconnections and the general architecture of systems, rather than on the individual components.

It is a change of perspective in the forma mentis of scientists rather than a new scientific discipline. Traditional science is based on reductionistic reasoning for which, if one knows the basic elements of a system, it is possible to predict its behavior and properties. It is easy to realise, however, that for a cell or for socioeconomic dynamics one faces a new situation in which the knowledge of the individual parts is not sufficient to describe the global behavior of the structure.

We can represent this situation as the study of the architecture of matter and nature. It depends in some way on the individual elements but then it shows fundamental laws and properties which cannot be derived from these elements. Starting from the simplest physical systems, these emergent behaviors can be identified in many other systems, from ecology to the immunitary system to social behavior and economics.

The science of complexity has the objective of understanding the properties of these systems. Which rules govern their behavior? How do they adapt to changing conditions? How can they learn efficiently and how do they optimize their behavior?

The development of the science of complexity cannot be reduced to a single theoretical or technological innovation but it implies a novel scientific approach with enormous potential to influence deeply scientific activities.