Gravitational waves from compact binary star systems

To be observed and analyzed by the gravitational wave detectors LIGO VIRGO on ground and LISA in space inspiralling compact binaries binary star systems composed of neutron stars and or black holes require high accuracy predictions from general relativity These very relativistic systems are accurately described by the post Newtonian approximation which is the flagship of approximation methods in general relativity In this talk after relevant motivating introduction we shall review the current state of the art on post Newto