On August 17, 2017 the Advanced LIGO and Advanced Virgo detectors discovered a gravitational-wave signal (GW170817) consistent with a binary neutron star (BNS) inspiral. Almost simultaneously, a gamma-ray burst (GRB 170817A) was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anticoincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. GW170817 is the loudest (highest signal-to-noise ratio) and closest gravitational-wave event observed so far. The LIGO and Virgo data produced a three-dimensional sky localization of the source, enabling a successful electromagnetic follow-up campaign that identified an associated electromagnetic transient in a galaxy ~40 Mpc from Earth. A multi-messenger view of GW170817 from ~100 seconds before merger through weeks afterward provides unprecedented insight into these events. For the first time, using gravitational waves we are able to constrain the equation of state of dense neutron stars and infer the rate of local binary neutron star mergers. When we include EM observations, we are able to independently measure the Hubble constant, probe the validity of the equivalence principle, gain new insight into the engine driving these events, and other ground-breaking fundamental results.