Astrophysical processes in compact stars can be largely divided into two classes, namely radiative and material. Due to extremely strong gravitational field of these stars both type of processes are effected by the gravitational field of the compact object. In theses cases the Newtonian approximation to the gravitational field breaks up and the relativistically correct laws must be used to describe any phenomenon related to compact stars. Gravitoelectromagnetic approximation provides such a frame-work. This monograph discusses the gravitoelectromagnetic approximation and its implications for compact star astrophysics. Since these stars rotate at angular speeds far below that of the speed of light, the processes occurring in these stars offer perfect conditions where the gravitoelectromagnetic approximation can be usefully employed and observationally tested. This book also contains an especially clear introduction to compact star astrophysics, and gives a fairly complete review of basic relativistic astrophysics.