This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated, solvability of operator equations in Banach spaces, linear operators in Hilbert spaces and spectral theory, Schauder's theory of linear elliptic differential equations, weak solutions of differential equations, nonlinear partial differential equations and characteristics, nonlinear elliptic systems, and boundary value problems from differential geometry.