A system of N non-relativistic classical particles interacting with pair potentials is described by a Hamiltonian of the form (0.0.1) This Hamiltonian generates a flow [(t) on the phase space JR3N x JR3N. An analogous system of N quantum particles is described by a Hamiltonian of the form N 1 H: = -L -Llj ] L \lij(Xi - Xj)' (0.0.2) j=l 2mj l$i

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This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.

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