The purpose of this thesis was to use the theory of transformation optics (TO) to control light along non-Euclidean surfaces. Chapter 2 provides an introduction to the fundamental theory of TO, the basics of non-Euclidean geometries, and a broad chronological overview of TO from its inception to the time this thesis was written. Chapter 3 details a novel application of Fermat's principle to cloak rotationally symmetric surface deformations from surface waves using an isotropic, all-dielectric, electrically thin material overlay. Also in this chapter, a realizable surface wave cloaking device is designed and its performance is validated. Chapter 4 builds directly upon Chapter 3 and describes how to map a rotationally symmetric at lens onto a rotationally symmetric surface deformation via an isotropic, all-dielectric, electrically thin material overlay. This chapter also includes the design and validation of two realizable surface wave lenses borne out of this approach. Chapter 5 addresses the primary limiting design factor found in Chapter 3 and 4 (rotational symmetry), by deriving from Maxwell's equations, an equivalence to handle rotationally asymmetric or more generally `arbitrary' surfaces. This work is signi cant because it provides a truly general solution to the problem of creating cloaks and illusion devices for surface wave applications. Finally, in Chapter 6 for the rst time, a direct comparative study of two distinct surface wave cloaking techniques, from Chapter 3 and Chapter 5, is conducted and the results are examined.