The consequences of Special Relativity follow from the assertion that the laws of physics are the same in all inertial frames. In particular, the speed of light is a limiting constant in all such frames. The consequences, deduced from this assertion, make up a body of results that have been repeatedly affirmed in practice since the early 20th century. I once tried to describe some of these consequences in a paper I wrote in a Philosophy of Science class. The professor gave me an A on the paper but asked, in the end, do these things really happen?
This paper,
Special Relativity Primer, explains the basic theory and provides exampes and worked exercises demonstrating the consequences.