Abstract:In this talk I will discuss the curvature structure of a 4-dimensional Lorentz manifold as used in Einstein’s General Theory of Relativity. The idea is to relate the ideas of metric, connection, curvature tensor, sectional curvature and geodesic structure on such a manifold and to discuss their interpretation in Einstein’s theory. It will be shown that, in the general case, these concepts are very closely related. The role of holonomy theory in the proofs will be mentioned. As a side result, some theorems on the relationships between certain symmetries in general relativity will be described.