The final piece of the puzzle falls in place. Herman Minkowski showed that Special Relativity defines a spacetime invariant - the "proper time" - between two events. Einstein's insight into the equivalence between falling and floating allowed him to realize that this also applied to General Relativity. All the techniques of differential geometry can now be applied to spacetime physics, and we arrive at the complete theory (at least for the empty space outside of matter).
Relativity playlist: http://www.youtube.com/playlist?list=PLF56602BAC693237E
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Playlist videos for General Theory of Relativity: