These lectures aim at providing an introduction to the properties of gravitational
waves and in particular to those gravitational waves that are expected as a consequence
of perturbations of black holes and neutron stars. Imprinted in the gravitational ra-
radiation emitted by these objects is, in fact, a wealth of physical information. In the
case of black holes, a detailed knowledge of the gravitational radiation emitted as a
response to perturbations will reveal us important details about their mass and spin,
but also about the fundamental properties of the event horizon. In the case of neutron
stars, on the other hand, this information can provide a detailed map of their internal
structure and tell us about the equation of state of matter at very high density, thus
filling-in a gap in energies and densities that cannot be investigated by experiments in
terrestrial laboratories.