This volume consists of the lecture notes of a Summer School dedicated to one of the proponents and first Chairman of the Strategy Board of MACSI-net, the late Jacques Luis Lions. MACSI-net is a European Network of Excellence, where both enterprises and university institutions co-operate to solve challenging problems to their mutual benefit. In particular, the network focuses on strategies to enhance interactions between industry and academia. It was set up by a joint effort of ECCOMAS and ECMI European associations. This particular event took place from March 17-22, 2003. It was a joint effort of the Training Committee and Industrial Relation Committee of MACSInet to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of industrial interest. The mastering of complexity implies the sharing of different tools by different actors which require much higher level of communication between people from different cultural backgrounds. Important examples of such interdisciplinary needs came from environmental problems (pollution of coastal waters due to oil spill, air quality of big cities, noise reduction, air/ocean interface, etc); quality of life (bioengineering of tissues and prostheses, air raffic control for safety, etc.); material science and metallurgy ( polymers, steel, etc); Aeronautics (multidisciplinary design optimisation, including aerodynamic efficiency, drag reduction, aero- and vibroacoustics, aeroelasticity - flutter, thermal flows, UAV trajectory control, etc) The need of facing multidisciplinary optimisation methods for multiphysics problems raises complex problems with respect to the following aspects: multiple scales (homogenisation, boundary layers, asymptotics, etc); variable stochastic geometries (interfaces, domain decomposition, etc); nonlinear reaction-advection-diffusion systems; stochastic differential systems; innovative inverse and optimisation algorithms because of multicriteria related to multisystem approach (evolutionary algorithms such as genetic algorithms, ant systems, game theory, hybrid methods, etc); optimal control ( level set--Hamilton-Jacobi-- methods, nature inspired methods such as ant systems, hybrid methods, etc.); strong coupling of several software systems (numerical analysis algorithms and CAD /CAM geometry tools); mathematical methods for visualisation.