Our perception of the physical world around us can be captured by the surfaces of objects. We have intuitive notions of smoothness or curvature of surfaces. In mathematics, surfaces appear as ideal objects which have been studied by classical smooth analysis for centuries. Surfaces are ubiquitous in applications such as scientific computations and simulations, computer aided design, medical imaging, visualization or computer graphics. For instance, in virtual reality, a scene is usually modeled with objects described by their boundary surfaces. In geometric computer processing, surfaces have to be described as discrete objects and many different discretizations are used. These applications require some knowledge of the surfaces processed: their topology, as well as local and global descriptions from differential geometry.