The objective of this text is to develop the theory of social health insurance (SHI; the expression used especially in the United States is “public health insurance,” which will be viewed as one variant of SHI here). While a good deal is known about the demand and supply of private insurance, the theoretical basis of SHI is much more fragile. Specifically, on the demand side, what are the reasons for social (or public) health insurance to exist, even to dominate private health insurance in most developed countries? With regard to supply, what do we know about the objectives and constraints of SHI managers? Finally, economists can predict properties of the equilibrium characterizing private health insurance (PHI). However, what is the likely outcome (“performance”) of SHI? At the normative level, one may ask, Should the balance be shifted from SHI to PHI?