  This review introduces the elasticity theory of two-dimensional crystals and
nematic liquid crystals on curved surfaces, the energetics of topological
defects (disclinations, dislocations and pleats) in these ordered phases, and
the interaction of defects with the underlying curvature. This chapter
concludes with two cases of three-dimensional nematic phases confined to spaces
with curved boundaries, namely a torus and a spherical shell.
