Partial Differential Equations and Complex Analysis is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and he examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the d-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.