The main objective of general relativity is to determine the metric that is generated by a given distribution of masses and energy, and then to explore the physics of this spacetime, e.g., by investigating the motion of objects or the propagation of light. An ingenious summary of this problem is due to Wheeler: Matter tells space how to curve and spacetime tells matter how to move! This requires an equation that links the metric of the spacetime to the distribution of masses and energy. Before we come to the formulation of this equation, we examine the non-relativistic approximation of the equations of motion in GR. The results will be of help in the subsequent analysis. From the quote just given we can already see an important property of gravitation, namely, the way it is treated in general relativity. The statement that matter curves spacetime and that this curvature in turn determines the motion of matter, which again has an impact on spacetime, indicates that the field equations will be non-linear differential equations, the solution of which will be possible only approximately in most of the cases.