This book is an attempt to make available to the student a coherent modern view of the theory of partial differential equations. Here equations of the first order and linear second order equations are treated with the tensor calculus, which combines generality and insight, in mind. Since the book is self-contained, much of the material is classical, but an effort has been made to achieve a modern outlook on these topics. A number of significant recent developments are introduced, and treated in relation to the natural background formed by geometry and physics.

Special features of the exposition are: (a) the simplified general treatment of first order equations; (b) the geometrical foundations of the theory of linear second order equations (c) unified treatment of boundary value problems and related topics by integral equations; (d) the theory of generalized hyperbolic potentials.

G.F.D. Duff (1929-2001) was a professor of mathematics at the University of Toronto and served as chair of the Department of Mathematics from 1968 to 1975. His mathematical interests were centered in the theory of differential equations, and he also worked in the theory of harmonic integrals.

G.F.D. Duff's profile page