The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems. A thorough discussion of multi-dimensional boundary value problems then introduces the reader to the fundamental partial differential equations and special functions of mathematical physics. Moving to non-homogeneous boundary value problems the reader is presented with an analysis of Green's functions from both analytical and algebraic points of view. This leads to a concluding chapter on integral equations.