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Nonadiabatic transition is a highly multidisciplinary concept and phenomenon, constituting a fundamental mechanism of state and phase changes in various dynamical processes of physics, chemistry and biology, such as molecular dynamics, energy relaxation, chemical reaction, and electron and proton transfer. Control of molecular processes by laser fields is also an example of time-dependent nonadiabatic transition. Thus, nonadiabatic transition represents one of the very basic mechanisms of the mutability of the world. This book has been written because the complete analytical solutions to the basic problem have recently been formulated by the author.