This lecture overviews the relation between matter and system complexity on one hand and Life, Intelligence and Environment on the other one. First the theoretical tools (systems, graph and  network theory) are overviewed. Then their relation to:  a) life structure, c) biological neural networks, c) AI and artificial neural networks, d) social structure and evolution and e) environment is presented. System and matter complexity measures are investigated and the Law of Complexity is presented. Finally, philosophical issues related to life evolution-by-design are introduced.