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This talk will discuss some of the geometrical ideas behind Einstein's general theory of relativity. It will consider the foundations of the general theory and Einstein's attempt to build his gravitational field equations using the 4-dimensional space-time ideas generated by his special theory (as finalised by Minkowski), together with those facets of Newtonian gravitation theory which he wished to retain and the classical differential geometry developed by Riemann.
Some simple, more modern developments will also be incorporated into the talk. These concern the possibilities for the field equations, Einstein's geodesic hypothesis regarding the motion of free particles in a gravitational field and the use of Killing symmetry in differential geometry to establish the theory of cosmology and wave theory.