Pulsating stars are important sources of information for
astrophysics. Nearly every star undergoes some kind of pulsation
during its evolution from the early stages of formation until the
very late stages, usually the catastrophic creation of a compact
object (white dwarf, neutron star or black hole). Pulsations of
supercompact objects are of great importance for relativistic
astrophysics since these pulsations are accompanied by the
emission of gravitational radiation. Neutron star oscillations
were also proposed to explain the quasi-periodic variability
found in radio-pulsar and X-ray burster signals [206,
146]. In this chapter we shall discuss various features of neutron
star non-radial pulsations i.e. the various modes of pulsation,
mode excitation, detection probability and the possibility to
extract information (to estimate, for example, the radius, mass
and stellar equation of state) from the detection of the
associated gravitational waves. It is not in our plans to discuss
rotating relativistic stars; the interested reader should refer
to another review in this journal [192]. Radial oscillations are also not discussed since they are not
interesting for gravitational wave research.