A CRT network on 'Complex Systems' is presently being formed- it will begin operations this summer. The main goal of this programme will be the study of a whole range of topics in physics, chemistry, and biology, which are unified theoretically by ideas which have come out of the study of complex physical and biological systems, often far from equilibrium, and the dynamics of complex networks. Examples in physics include the study of glasses (classical and quantum), diffusion on graphs and fractal systems, self-organising and multi-critical systems, and the electronic properties of complex new materials, in solid-state physics and the physics of soft matter- particular emphasis will be given to new quantum materials. This last theme also relates to work done in quantum chemistry on complex molecules and their organisation and assembly, to protein folding, etc., and to organisational structures in genetics and protemics. Finally there are similar themes in theoretical biology, and computer science- eg., the dynamics of branching networks like the internet.