The emergence and spectacularly rapid evolution of the field of atomic and molecular clusters are among the most exciting developments in the recent history of natural sciences. The field of clusters expands into the traditional disciplines of physics, chemistry, materials science, and biology, yet in many respects it forms a cognition area of its own. This book presents a cross section of theoretical approaches and their applications in studies of different cluster systems. The contributions are written by experts in the respective areas. The systems discussed range from weakly (van der Waals) bonded, through hydrogen- and covalently bonded, to semiconductor and metallic clusters. The theoretical approaches involve high-level electronic structure computations, more approximate electronic structure treatments, use of semiempirical potentials, dynamical and statistical analyses, and illustrate the utility of both classical and quantum mechanical concepts.