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There’s not just one theory of relativity, but two! Special relativity (Einstein’s theory of special relativity, or SR for short) and General relativity (Einstein’s theory of general relativity, or GR for short).
Actually, that’s not quite right either; it’s Einstein’s two theories most people mean when they talk about ‘the theory of relativity’ (well, most of the time), but Newtonian mechanics is also a theory of relativity. Basically, a theory of relativity starts with assumptions like the laws of physics being the same no matter who measures them (i.e. independent of the observer), and when they are measured (this is closely related to the conservation of energy, via a powerful theorem by Emmy Noether). So Galilean relativity says that the laws of physics are the same for all inertial observers, Newtonian relativity adds that there is an absolute space (in which the laws of nature formulated by Newton hold) and an absolute time (for all inertial observers).
Einstein’s special theory of relativity is quite similar to Newtonian relativity; both refer to inertial observers, and both assume (‘postulate’) that (certain) laws of nature will be the same to all such observers. However, SR goes further than Newton did, by referring to all laws of nature (Newtonian relativity doesn’t apply to electromagnetism, for example), but the big difference is the SR postulate that the speed of light (in a vacuum) is the same for all inertial observers … this means there is no absolute space, or time (and also that you can’t go faster than c).
General relativity is more general than special relativity (duh!) … it applies to all observers (not just inertial ones). It also adds a postulate concerning mass and gravity, neatly summed up by John Wheeler as “spacetime tells matter how to move; matter tells spacetime how to curve“.
UCLA’s Ned Wright has one of the best introductions to the theory of relativity (both of them!), with particular emphasis on astronomy and cosmology: Relativity Tutorial. For a fun introduction (“In Words of Four Letters or Less”), Albert Einstein’s Theory of Relativity from Muppetlabs is cool! Of course, there’s a lot more out there on the internet, much of it very good (but some, sadly, is just plain nonsense … for some reason relativity is a magnet for crackpot ideas).
Pulsars Confirm Einstein’s Theories, Einstein Still Rules Says Fermi Telescope Team, Theory of Relativity Passes Another Test … that’s just a small selection of what Universe Today has to offer on the theory of relativity (both of them).