This lecture will be an intuitive, geometrical approach to the concept of curvature. Beginning from two-dimensional curvature, it will then go on to discuss space curves and curved surfaces. We will consider the major results of Gauss' General Investigations of Curved Surfaces, in particular the Theorema Egregium, showing that curvature is an intrinsic property of surfaces. At the end we will consider the importance of Gauss' work for non-Euclidean geometry (Lobachevsky) and Einstein's theory of general relativity.