This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW astronomy, from Einstein’s prediction of GWs in 1916 to the first direct detection in 2015. It presents the theory of linearized perturbations about Minkowski spacetime of Einstein’s equations, and shows how gauge transformations reduce the problem to the standard wave equation with two degrees of freedom, or polarizations, h_+,h_×. We derive the quadrupole formula, which relates the motion of matter in a source region to the far GW field. It is shown that GWs carry energy, as well as linear and angular momentum, away from a source. The GW field of an orbiting circular binary is found; and properties of the evolution of the binary including rate of inspiral and time to coalescence, are calculated. A brief review is given of existing and proposed GW detectors, and of how to estimate source parameters in LIGO or Virgo data of a GW event. The contributions that GW observations have already made to physics, astrophysics and cosmology are discussed.