After many years of effort, Einstein discovered the general theory of relativity, the extension of special relativity to include the force of gravity. To do this, he extended the four-vector structure of special relativity to more general Riemannian geometries in which space-time is bent under the influence of gravity. The theory has successfully passed all the high precision tests now available. Predictions include the existence of black holes and gravitational waves. Both have now been convincingly observed. In this chapter, the basic concepts behind the theory are described and then illustrated by analysis of the Schwarzschild metric.