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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* boundary value problems from differential geometry This new second edition of this volume has been thoroughly revised and a new chapter on boundary value problems from differential geometry has been added. In the first volume, partial differential equations by integral representations are treated in a classical way. This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.