Gravitational waves (GW) are solutions of the field equations of Einsteins’ general relativity (GR) and can be thought of as propagating ripples in spacetime. Since the first direct detection of a GW signal by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015, the study of gravitational waves has become a new focus of mathematical physics.

In this signature work, we review the detection of GW and concentrate on the underlying theory provided by Einstein’s theory of GR. Specifically, we develop the required differential geometry from first principles in order to derive the GW equation from GR. This shows that the speed of GW equals the speed of light. We also discuss the observational corroboration of this remarkable result.