This chapter is devoted to a formulation of Einstein’s Theory of Gravitation using the mathematical language developed in Chaps. 2 – 12 for describing the intrinsic “geometries” of different differentiable manifolds. Einsteinian spacetimes are defined in terms of a 4-dimensional metric tensor field with Lorentzian signature, a Levi-Civita connection and a symmetric, divergenceless, type- \((2,0)\) source tensor for the Einstein equation (Sect. 15.1 ). The existence of a spacetime with a timelike Killing vector field is shown to be necessary in order to define spacelike hypersurfaces on which idealised clocks can be synchronised. A precise definition of “freely falling” observers is given in terms of timelike geodesic observer curves and conditions are derived for observers with arbitrary 4-acceleration to be “stationary” or “static” (see also Sect. 15.1 ). Furthermore, given a particular solution to Einstein’s gravitational field equation, the construction of a comoving reference Frame is carried out. Within this framework the notion of a “material clock” is discussed in Sect. 13.1. The notion of “time” measured by a material clock is then discussed in the context of the “clock hypothesis” in Sect. 13.2.