Recent years have witnessed a resurgence in the kinetic approach to dynamic many-body problems. Modern kinetic theory offers a unifying theoretical framework within which a great variety of seemingly unrelated systems can be explored in a coherent way. Kinetic methods are currently being applied in such areas as the dynamics of colloidal suspensions, granular material flow, electron transport in mesoscopic systems, the calculation of Lyapunov exponents and other properties of classical many-body systems characterised by chaotic behaviour. The present work focuses on Brownian motion, dynamical systems, granular flows, and quantum kinetic theory.