Einstein's general theory of relativity

Einstein's general theory of relativity states that gravity is not a force, but is a consequence of a curved space-time. This is our space-time “warped” by the mass and energy within it.

Space-time is the playing field in which all events take place. Every point, from the origin of the universe to the end of the universe, is given by three space coordinates and one time coordinate. But, as Stephen Hawking says, in A Brief History of Time, "it is impossible to imagine a four-dimensional space. I personally find it hard enough to visualize three-dimensional space!"

Objects are not pulled by the force of gravity, but follow a geodesic -- the shortest path in a curved space. 

The earth's surface is a two-dimensional curved space, and its geodesics are great circles. In Einstein's general theory of relativity, bodies follow straight lines in four-dimensional space-time, but appear to us to move along curved paths in 3D space.

The orbits of the planets predicted by Einstein's general theory of relativity are almost the same as those predicted by Newton's universal law of gravitation. However, Einstein's general theory of relativity predicts that the long axis of the elliptical orbit of Mercury should rotate about the sun at about one degree every ten thousand years. This "precession of the perihelion of Mercury" had been noticed before 1915, and helped confirm Einstein's general theory of relativity. Recently, radar measurements of the orbits of the other planets has provided further confirmation.

Light rays must also follow geodesics in space-time. General relativity predicts that light from a distant star that passes near the sun should be deflected slightly. It is usually difficult to see this effect, because the light from the sun makes it impossible to see the stars! However, you can see them during an eclipse of the sun. In 1919 a British expedition, led by Sir Arthur Eddington, observed an eclipse from West Africa, showed that light was deflected just as predicted by general relativity.

To someone on a high tower everything on the ground looks to take longer than on the tower - general relativity predicts that time slows when gravity strengthens. This prediction was tested in 1962 using very accurate clocks, and Einstein's general theory of relativity stood the test. If navigation satellites ignored the predictions of general relativity, their calculations would be several miles out.

The demands of Newton's universal law of gravitation demanded an absolute space and absolute time which were not affected by gravitating bodies. But the general theory of relativity showed that moving or gravitating bodies warped space and time, and space-time affected the way in which bodies moved. Stephen Hawking said: "Just as one cannot talk about events in the universe without the notions of space and time, so in general relativity it became meaningless to talk about space and time outside the limits of the universe. The old idea of an essentially unchanging universe that could have existed, and could continue to exist, forever was replaced by the notion of a dynamic, expanding universe that seemed to have begun a finite time ago...Roger Penrose and I showed that Einstein’s general theory of relativity implied that the universe must have a beginning..."A Brief History of Time by Stephen Hawking, chapter 2.

Einstein’s general theory of relativity is a classical theory, because it ignores Heisenberg's uncertainty principle, which states that the more accurately you measure a particle's position, the less accurately you can measure its momentum.

No discrepancy of Einstein’s general theory of relativity with observation has been observed, but we have never observed the strongest gravitational fields. These occur near black holes and the big bang singularity. In these situations, quantum mechanics becomes important. This has led to attempts to understand the forces of nature in a unified theory of physics. But, as yet, this remain unsuccessful and Einstein’s general theory of relativity is still the most fundamental, generally accepted, theory of gravity

Einstein's general theory of relativity further reading:

The Road to Reality by Roger Penrose