The Theory of Relativity started from the famous Michelson-Morley experiment in 1900 when several physicists were looking for a physical concept to explain the constancy of the speed of light
Some of them (Lorentz, Heaviside, Lodge, Fitzgerald, Lamor, and Einstein) explained the null effect of the Michelson-Morley experiment by the contraction of matter at movement. Two of them (Lamor and Einstein) integrated the fact into the theory that there is a different progress of time in different moving frames. These is how the Relativity Theory came out.There have already been numerous experiments conducted since 1905 to prove the Relativity Theory.
The following web-page contains the English translation of original paper on the Special Theory of Relativity published by Einsten in June 1905.
http://www.fourmilab.ch/etexts/einstein/specrel/www/