Schwarzschild spacetime is the first non trivial solution of the Einstein vacuum equations to have been constructed. Schwarzschild’s result is meant as a rigorous reworking of Einstein’s proof of the advance of Mercury’s perihelion (published November 1915). Instead of Einstein’s perturbative approach, Schwarzschild described the gravitational field of a spherical massive object (the sun in Mercury’s case) as an exact solution of Einstein’s equations in the vacuum. He wrote to Einstein in December 1916 to tell him about his result, which Einstein presented in front of the Prussian academy in January 1916. Schwarzschild’s metric is now fully understood as describing the geometry of a spacetime containing a spherical eternal black hole. But at the time, the metric puzzled many people because it appeared to contain a singularity not only at the origin but also on a finite sphere within the spacetime. We shall describe the metric and construct the maximally extended spacetime, understanding the nature of the event horizon along the way.