What is the basic assumption(s) required to explore general relativity?
For example, if one merely assumes that the speed of light $c$ is the same for all observers, and the laws of physics are the same for all observers, then it's possible using a mix of algebra and some calculus to derive every SR result from time dilation to length contraction, $E = mc^2$, and so on.
What is the basic premise of general relativity? I assume that all of SR is included but is there anything else?
The basic premise behind general relativity is the equivalence principle, the idea that an object moving in an accelerating (non-inertial) reference frame is indistinguishable from one moving under the influence of a gravitational field.
(As an aside, Einstein's original proofs of time dilation, length contraction, even $E=mc^2$ don't involve any calculus - they are quite simple and elegant. GR on the other hand is rather calculus-intensive)
What is the basic premise of general relativity?
It just might be general covariance even if the content of that phrase is controversial. For example:
Einstein offered the principle of general covariance as the fundamental physical principle of his general theory of relativity and as responsible for extending the principle of relativity to accelerated motion. This view was disputed almost immediately with the counter-claim that the principle was no relativity principle and was physically vacuous. The disagreement persists today.
