  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, $h_+,h_\times$. 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.
