Special: light travels at a constant speed for all observers, plus the laws of motion are the same in all inertial (non-accelerating) frames. Makes all physical laws “covariant” (really invariant) under a certain group of coordinate transformations. Encodes quantities like energy and momentum with scalars and 4-vectors. Models spacetime as a manifold that is locally \({\mathbf{R}}^3 \times{\mathbf{R}}\) with metric signature \((+,-,-,-)\). Works for reformulating classical laws, but doesn’t incorporate gravity.
General: Want a theory that works for accelerating frames and incorporates gravity. Requires bringing together energy, momentum, stress, and pressure, and moving to \(4\times4\) tensors instead of 4-vectors. Recover SR by defining inertial frames to travel along geodesics with constant velocity (setting acceleration equal to zero).