The SPIDER IRSES aims to draw together the complementary knowledge, know-how, methodology and skills of 5 EU teams with 6 carefully selected non-EU groups to tackle problems at the forefront of contemporary research into complex systems. These are in the overlapping themes of complex bio- socio- and materials science.The notion of soft matter subsumes a wide range of systems that traditionally were referred to as chemical and biological objects. These include simple and molecular liquids, electrolyte melts and solutions, polymers, polyelectrolytes, liquid crystals, gels, membranes, various biological systems, amorphous and glass-like materials, and granular matter. The aim of our study is to analyse soft-matter phenomena, in particular polymers and proteins. The second main theme of SPIDER is collective critical phenomena on complex systems and networks. Here we will tackle both physical and sociological systems.In all cases we are interested in how the behaviour of macroscopic systems emerges from agents (fundamental biological, physical or sociological entities) and how the properties of the whole are different to the sums of the properties of component parts. Here we are especially interested in the concept of universality, by which the emergent phenomena are largely independent of many of the microscopic details of the systems. Of particular interest in modern research into emergence of life itself are self-organised systems and their responsive behaviour.Owing to the large number of microscopic agents involved, the methods of statistical physics are ideal to tackle emergent-phenomena problems. Both numerical and analytic (including exact) approaches are envisaged. A complete set of tools (theory and extensive numerical simulations) is equired to solve these problems. Such a set is not available to any of the EU partners individually, and in order to achieve this goal, groups from Argentina, Brazil and Russia have been carefully selected.