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, 147]. 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 . Radial oscillations are also not discussed since they are not interesting for gravitational wave research.
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