  We study the pages in Albert Einstein's 1916 landmark paper in the Annalen
der Physik where he derived his field equations for gravity. Einstein made two
heuristic and physically insightful steps. The first was to obtain the field
equations in vacuum in a rather geometric fashion. The second step was
obtaining the field equations in the presence of matter from the field
equations in vacuum. (This transition is an essential principle in physics,
much as the principle of local gauge invariance in quantum field theory.) To
this end, we go over some quick differential geometric background related to
curvilinear coordinates, vectors, tensors, metric tensor, Christoffel symbols,
Riemann curvature tensor, Ricci tensor, and see how Einstein used geometry to
model gravity.
