Leonard Susskind does 8 lectures on general relativity. I think lecture 1 can probably be skipped (that's an opinion mind you). Anyways, the takeaway from lecture 2 is that curvature is an obstruction to finding a flat metric, or rather to finding a way to define distances between points which requires only Pythagoras. That is, (being able to define) a 'surface' which can have coordinates defined on it which are rectilinear. The other is that a gravitational source is a spherical body with mass. The obstruction is that tidal forces exist because the field around such a body diverges, so you can't transform (except over small regions) to an accelerated frame which is in free fall (such that gravity vanishes)--the equivalence principle applies in a strictly local sense, trying to make it global encounters the obstruction (tidal forces due to divergence). Then there is some stuff Gerard t'Hooft wrote in SciAm about what happens when you take a global symmetry and try to make it a local symmetry, which requires the addition of a 'force' to restore the symmetry (the global symmetry recall, is the spherical shape of gravitational sources, locally over small distances and times, this symmetry breaks because it looks flat). Or something like that. Another thing, the general theory says nothing else about the structure of bodies with mass (acceleration in a gravitational field is independent of the 'material nature' of a body with mass), that is, it says nothing about the structure of matter fields, treating them only as densities. The other big theory we have, quantum mechanics, says nothing about what a physical measurement is (in accelerated or inertial frames; frames don't really exist in QM, we have to invent them to do experiments), in fact that theory isn't physical at all; it's about complex amplitudes which define probabilities, right? So that there's a gap between these two theories seems obvious, maybe. No takeaway there, however.