The science of complex systems is no longer new, and it is therefore appropriate to critically analyze some of the major results which have been achieved. A brief sketch of the development of complex systems science is presented, followed by a discussion of some of its core concepts (the emphasis is on concepts rather than on tools and specific applications). The viewpoint taken in this paper is that complexity science is concerned with the organization properties of nonlinear systems, and on concepts which are general enough to hold for wide classes of systems. A discussion of the relevance of complexity for the study of social systems is also presented as well as some remarks concerning possible future developments.
