This volume collects a number of contributions on the general theme of spontaneous symmetry breaking in nonlinear systems, and related topics. Current studies in these areas are going ahead at a full speed. Chapters included into the book present an overview on major recent achievements. They cover a number of different physical settings, which are introduced when a nonlinearity is added to underlying symmetric configurations. The spontaneous symmetry breaking, alias self-trapping into asymmetric states, happens when the strength of the nonlinearity exceeds a certain critical value. A related generic dynamical effect appears in the form of Josephson oscillations between mutually symmetric states. Theoretical studies of these phenomena, as well as related experimental findings, are extensively discussed in the book - chiefly, in the context of Bose-Einstein condensates and nonlinear optics.