Einstein's special relativity was "special" because it dealt only with the specific case of intertial reference frames. An inertial reference frame is a body that is either at rest or that moves with a constant velocity. In contrast, his general theory of relativity accounts not only for these, but also for bodies that accelerate (i.e., change their velocity). Einstein began his theory with a thought experiment--that is, an experiment carried out only in the mind of the experimenter. This experiment imagines a physicist in a room on Earth dropping a ball to the ground. The ball falls to the floor at an accelerating rate because of the force of gravity. (link here) However, the physicist would observe the same phenomenon in an accelerating spaceship in a region of outer space without gravity: upon the ball's release, it would hang suspended in mid-air as the floor of the spaceship rushed up to hit it. To the physicist inside the ship, however, the ball would appear to "fall" toward the floor exactly as it did in the room on earth. Thus, it would be impossible for the physicist inside the spaceship to distinguish between gravitation and any other acceleration. Indeed, this was the essence of Einstein's "equivalence principle," which posits the equivalence of physical effects within reference frames at rest within a gravitational field (like the room) and within reference frames accelerating in the absence of any gravitational field (as in the rocket). The equivalence principle also posits the equivalence of gravitational mass (the measure of the force a body exerts on another) and inertial mass (the measure of a body's resistance to being accelerated).

Based on this principle, Einstein formulated the principle of general covariance, which forms the basis of his general theory of relativity. This maxim states that the laws of physics are the same in all (i.e., both inertial and gravitational) reference frames. This extends the first postulate of special relativity to include accelerating frames of reference as well. Basically, with his general covariance principle, Einstein applied the equivalence principle to special relativity: given that the laws of physics are the same in all inertial reference frames and that inertial and gravitational masses are equivalent, the laws of physics are the same in all accelerating frames as well.

One consequence of this principle is that space-time in the presence of matter is curved. (Space-time is the four-dimensional continuum of time and space in which any event or physical object is located.) This can be understood by imagining a spaceship accelerating upward through space. If a light ray enters the ship through a window, a person inside the ship will see the light ray bend downward, because by the time the light reaches the other wall of the spaceship, that wall will have accelerated upward; thus the ray of light enters through the window at one height, and hits the opposite wall at a height closer to the floor of the space ship. Yet because nothing can travel faster than light, we know that light must always travel the shortest distance between two points; and since the shortest distance between two points in an accelerating spaceship is curved, space-time itself must be curved. As Einstein demonstrated, mass causes a curvature in space-time in much the same way as a bowling ball will deform the shape of a stretched rubber sheet on which it rests. Rather than speaking in terms of mysterious forces of attraction, as Newton did, Einstein understood gravitation as pure geometry. With the help of his mathematician friends Minkowski and Grossman, he was able to quantify the extent to which a body warps its surrounding space-time.

After completing the general theory of relativity, Einstein began working on a clear and comprehensive presentation of it. Until this point, most of his publications were provisional reports on the state of his research, comprehensible only to those physicists who had been following his work all along. In 1916, he published a treatise entitled "Foundations of the General Theory of Relativity," in which he established the terminology of "special" and "general" relativity and presented his theory formally. Then, at the end of 1916, he published a small book entitled On the Special and the General Theory of Relativity, Generally Comprehensible. This work was written with as little mathematics as possible and was designed to appeal to an even broader readership, albeit one still somewhat educated in mathematics or physics.

After arriving at the final form of his theory of general relativity in November 1915, Einstein proposed three possible tests for his theory. These involved the orbit of the planet Mercury, the bending of starlight near the sun, and the redshift of light. Though all of these tests were successfully executed to confirm Einstein's theory, it was the second test that garnered the most attention and catapulted Einstein into international prominence. On November 6, 1919, a team of British astronomers led by Arthur Eddington reported to the Royal Society of London that during a recent total eclipse of the sun, they had observed that the positions of the stars near the sun appeared to have shifted slightly from their proper positions. The amount of bending was fully consistent with Einstein's theory of relativity. The publication of this finding in newspapers across the world made Einstein an immediate celebrity. The story was even more sensational considering that a German physicist's theory had been confirmed by a team of British astronomers just after World War I. Thus, of all of Einstein's numerous contributions to physics, it was general relativity that first won him the widespread fame and recognition he would enjoy for the rest of his life.

However, not all the response to his theory was positive. In the early 1920s, a group of anti-Semitic fanatics led by Paul Weyland formed the "Study Group of German Natural Philosophers." The Study Group organized meetings across Germany, at which they denounced relativity as a "Jewish theory." Einstein published a scathing reply to their attack, and the group disbanded shortly thereafter. Unfortunately, this was not the last of the anti-Semitism that Einstein would encounter during his tenure at the University of Berlin.