Today a major trend in fundamental sciences is the study of nonlinear systems and the appearance of complex behavior. Such systems are characterized by many interacting entities as in macroscopic physics where systems composed of many microscopic particles present collective and nonlinear phenomena such as phase transitions, or transport properties under nonequilibrium conditions. As a starting point such a study requires the microscopic description in terms of interacting particles and the next step is to derive the collective and transport properties by mathematical methods.