Introduction -- Representation theory and the scattering operator -- A semigroup of operators related to the scattering matrix -- The translation representation for the solution of the wave equation in free space -- The solution of the wave equation in an exterior domain -- Symmetric hyperbolic systems, the acoustic equation with an indefinate energy form, and the Schrödinger equation -- Appendix 1. Semigroups of operators -- Appendix 2. Energy decay -- Appendix 3. Energy decay for star-shaped obstacles -- Appendix 4. Scattering theory for Maxwell's equations -- Epilogue.