The accomplishments and the available expertise of scientists working on spin systems, lattice gauge models, and quantum liquids and solids has culminated in an extraordinary opportunity for rapid and efficient development of realistic strategies and algorithms of ab initio theoretical analysis of conventional and exotic condensed-matter systems. This volume presents the latest results in the interdisciplinary field of lattice many-body systems. These include magnetism and phase transitions and lattice gauge problems in quantum field theory. Also treated are strongly correlated systems that help to unify many-body problems in solid-state physics, crystallography, and materials sciences and that helped their quantitative understanding.