I have read so many complicated description of whats theory of relativity that I tend to think such complicacy serves two purposes;
Misleading: it takes us away from the real concepts.
Complicated: It does not make the concepts easy at all to grasp.
Ineffective: It ill-prepares even very good students — as their precious time is wasted and the mediocre rejoice.
Here is an appropriate description of relativity theory.
Relative as suggests hinges on in reference to what? So you may call it a reference-dependent theory. But if you understand what theory of relativity is you may as well call it an equivalence theory.
This theory establishes for the first time in greater depth the equivalence of many ideas, concepts, physical laws and methods. This is the work of Albert Einstein. But if you dig deeper you will see that most of the concepts were known before, and classical physics is capable of producing these ideas 1st hand.
It is for no strange reason relativity theory is included as classical physics, in greater conceptual frameworks. Its because its merely a more refined calculation of certain problems, some of which were known and some which were not, but never to the extent and power of the methods of Einstein.
Einstein eg solved the problem of perihelion of mercury very exactly which was not as exactly understood in the canonical formulations of the old classical theory, so theory of relativity is the new classical theory.
But there are two episodes of this story.
1. Special theory of relativity: this is a regime of the theory of relativity where it pertains exclusively to kinetic energy: