In this lecture, Professor Susskind derives the metric for a gravitational field, and introduces the relativistic mathematics that describe a black hole. He begins by reviewing the concept of light cones and space- and time-like intervals from special relativity. He then moves on to review the flat space-time metric and geodesics, and the connection between the mathematics of geodesics and the Lagrangian formulation of classical mechanics. This leads to the mechanics of a particle moving in a gravitational field, and then to the derivation of the metric for a gravitational field, also known as the Schwarzschild metric. These are the fundamental mathematics that show the equivalence of a gravitational field and curved space-time.