There are two, theories of relativity, by Einstein, the special theory of relativity (or just special relativity, SR), and the general theory of relativity (or just general relativity, GR).
The special theory of relativity was published in 1905, in Annalen der Physik (“Zur Elektrodynamik bewegter Körper“, in the original German; “On the Electrodynamics of Moving Bodies” is its English translation), and the general theory of relativity published in 1915, in the Minutes of the Meetings of the Prussian Academy of Sciences (Berlin) (“Die Feldgleichungen der Gravitation” in the original German; “The Field Equations of Gravitation” is its English translation).
In its original form, special relativity is based on just two postulates (or assumptions); namely, that the speed of light (in a vacuum) is constant – no matter who measures it, or when, or where – and that the laws of physics are the same for in all inertial frames of reference (basically, for all observers who are not accelerating) … there are other, logically consistent, ways to construct SR, from different postulates, but they are equivalent to Einstein’s original.
The general principle of relativity at the heart of general relativity is easy to state (something like “the laws of nature are the same, everywhere, everywhen, and to everybody“), but the additional postulate (or postulates) is not. However, the consequence of this postulate is easy to say, in words – gravity is geometry … or in the words of John Wheeler “spacetime tells matter how to move; matter tells spacetime how to curve“.
Special relativity has been tested sixty ways to Sunday, and there are no experimental results which contradict it (or, rather, none which are reproducible). It is incorporated into all modern theories of physics, particularly quantum electrodynamics (which is the most precisely tested scientific theory, period), and general relativity. It is also (!) mathematically consistent (self-consistent, internally consistent), and reduces to Newtonian mechanics in the limit of small speeds.
General relativity has also been extensively tested, though not as thoroughly as special relativity (see The Confrontation between General Relativity and Experiment).
The internet has lots and lots of material on Einstein’s theories of relativity (but do be careful, some sites are overtly anti-science, and some are just crackpot nonsense); two examples of good summaries/intros: Albert Einstein and the Theory of Relativity (from the University of Tennessee), and Relativity Tutorial (Ned Wright, UCLA).
There are lots and lots (and lots and …) of Universe Today articles on Einstein’s theories of relativity; here is a sample: Einstein Still Rules Says Fermi Telescope Team, and New Way to Measure Curvature of Space Could Unite Gravity Theory.