I'm self-studying differential geometry using Lee's Intro to Smooth Manifold and Do Carmo's Riemannian Geometry. However, I've never studied the subject so-called "differential geometry of curves and surfaces" (such as the one dealt with by Do Carmo's Differential Geometry of Curves and Surfaces). Since this topic exclusively deals with 3-dimensional space, it doesn't attract me as much as other DG topics so far.
What's the point of studying this topic? How important is it for those who will later study more advanced DG, especially Riemannian Geometry? If you think it's a kind of an optional subject, what would you learn instead? If you think it's an integral part of DG sequence, could you give me the reason why it is so important as well as some of its interesting applications and theorems?