  Collective electronic excitations at metal surfaces are well known to play a
key role in a wide spectrum of science, ranging from physics and materials
science to biology. Here we focus on a theoretical description of the many-body
dynamical electronic response of solids, which underlines the existence of
various collective electronic excitations at metal surfaces, such as the
conventional surface plasmon, multipole plasmons, and the recently predicted
acoustic surface plasmon. We also review existing calculations, experimental
measurements, and applications.
