This chapter provides an overview of astrodynamics. Astrodynamics is the engineering or practical application of celestial mechanics and other allied fields, such as high-altitude aerodynamics, geophysics, and electromagnetic, optimization, observation, and navigation theory to the contemporary problems of space vehicles. Although two-body formulae are extremely useful for feasibility studies, when a definitive orbit computation is required, recourse must be taken to more sophisticated perturbation techniques. In general, perturbative forces can be defined as forces acting on an object other than those forces that cause it to move on some reference orbit. In the case of planetary motions, astronomers adopted the two-body elliptical motion of an object as the reference motion. Hence, all non-two-body forces such as those arising from the other planets are characterized as perturbative forces. There are roughly two approaches to the definitive computation of orbits. The first is termed general perturbations and involves the analytical integration of series expansions of the perturbative forces and is particularly useful in the computation of orbits extending over long periods, for example, in the case of earth satellites, the moon, and planetary trajectories. The second, termed special perturbations, refers to the computation of an orbit by numerical integration