In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The proofs are constructive so that the theory allows for efficient algorithms in order to compute the area of the SES and the volume of the SES-cavity, or to visualize the surface. Further, we propose to refine the notion of SAS and SES in order to take inner holes in a solute molecule into account or not.