In this chapter, we discuss several approaches to the problem of measuring how ‘curved’ a surface is. Although they use quite different methods, we show that each of the approaches leads to the same geometric object: the second fundamental form of a surface. It turns out (see Theorem 10.1.3) that a surface is determined up to an isometry of ℝ3 by its first and second fundamental forms, just as a unit-speed plane curve is determined up to an isometry of ℝ2 by its signed curvature.