the Einstein field equations
John Wheeler compressed the whole of general relativity into a sentence: matter tells spacetime how to curve, and spacetime tells matter how to move. The Einstein field equations are the first half made exact. They are the master law of gravitation, the relation that determines how much and in what way spacetime bends in response to the energy and momentum packed into it. Newton's law of gravity emerges from them as a gentle, slow, weak-field shadow of the full statement.
In compact form they read G_ab + Lambda g_ab = (8 pi G / c^4) T_ab, where G_ab is the Einstein tensor made of curvature, T_ab is the stress-energy tensor describing all matter and energy, Lambda is the cosmological constant, G is Newton's constant, and c the speed of light. This is ten coupled, nonlinear partial differential equations for the ten components of the metric. Because the Einstein tensor is automatically divergence-free, the equations enforce local conservation of energy and momentum, nabla^a T_ab = 0, as a built-in consequence rather than an extra assumption.
In the weak-field, slow-motion limit these equations collapse to Newton's, reproducing the Poisson equation for the gravitational potential, del^2 phi = 4 pi G rho, so general relativity contains Newtonian gravity as a special case. But it is crucial to be honest about what 'limit' means: the equations are genuinely nonlinear, gravity itself carries energy and so gravitates, and near black holes or in the early universe there is no small correction to Newton at all, the geometry is dominated by effects Newton's theory simply cannot express. General relativity is not Newton-plus-a-tweak; it is a different theory that happens to agree with Newton when gravity is weak and motions are slow.
Feed the field equations a spherical, non-rotating mass in empty surrounding space and, after solving the ten equations, out comes the Schwarzschild metric, which then predicts Mercury's extra orbital precession, the bending of starlight, and the existence of black holes, all from one law.
One law, many predictions: Schwarzschild and its classic tests follow.
The cosmological constant Lambda is the one term Einstein could add without spoiling the conservation property, since the metric itself is divergence-free. Today it is read as dark energy driving cosmic acceleration; Einstein first inserted it to force a static universe and later regretted it, but it was never mathematically illegitimate.