 The “geometrization of gravitational force” in 1915 gave the geometrization program its first, partial, realization as well as its subsequent impetus. In Einstein’s theory, the fundamental or “metric” tensor \(g_{\mu\nu}\) of Riemannian geometry appears in a dual role which thoroughly fuses its geometrical and its physical meanings. As is apparent from the expression for the differential interval between neighboring spacetime events, \(\textit{ds}^{2}= g_{\mu\nu} \textit{dx}^{\mu} \textit{dx}^{\nu}\) (here, and below there is an implicit summation over repeated upper and lower indices), the metric tensor is at once the geometrical quantity underlying measurable metrical relations of lengths and times. In this role it ties a mathematical theory of events in four-dimensional curved spacetime to observations and measurements in space and time. But it is also the potential of the gravitational (or “metrical”) field whose value, at any point of spacetime arises as a solution of the Einstein Field Equations (see below) for given physical quantities of mass-momentum-stress in the immediate surrounding region. In the new view, the idea of strength of gravitational force is replaced by that of degree of spacetime curvature. This curvature is manifested, for example, by the tidal force of the Earth’s gravitational field that occasions two freely falling bodies, released at a certain height and at fixed separation, to approach one another. A freely falling body (ideally, an uncharged test particle of negligible mass) in a gravitational field follows a geodesic path (that is, a curve of extremal length in a generally curved pseudo-Riemannian spacetime). The body is no longer to be regarded as moving through space according to the pull of an attractive gravitational force, but simply as tracing out the laziest (longest or slowest possible) four-dimensional trajectory between two finitely separated spacetime events. In consequence, in general relativity the equation of motion of a free body is a geodesic equation according to which the body’s spacetime (four-) acceleration vanishes identically and its free fall becomes indistinguishable from inertial motion. According to this equation, a free body moves on a geodesic path in both the presence and absence of a gravitational field. This is possible because the equation contains a multi-index term (not a tensor) called a connection allowing a gravitational field to appear or not according to a given choice of spacetime coordinates. As a result, in general relativity there is no observer-independent (coordinate-free) way to partition the combined inertial-gravitational field into its separate components. The gross mechanical properties of bodies, comprising all gravitational-inertial phenomena, can be derived as the solution of a single linked system of ten generally covariant partial differential equations, the Einstein equations. According to these equations, spacetime and matter stand in dynamical interaction. One abbreviate way of characterizing the dual role of the \(g_{\mu\nu}\) is to say that in the general theory of relativity, gravitation, which includes mechanics, has become geometrized, i.e., incorporated into the geometry of spacetime. Yet Einstein objected to claims that in general relativity gravitation is reduced to geometry as that statement’s natural interpretation severs the unification of inertia and gravitation that to Einstein comprised the theory’s core achievement.