Since their introduction in 1828, Green’s functions have become a fundamental mathematical technique for solving boundary-value problems. This book systematically presents the various methods for deriving these useful functions and leads readers through the process of developing Green’s functions for ordinary and partial differential equations. In addition to exploring the classical problems, the book includes special sections on leaky modes, water waves, and absolute/convective instability. With a wealth of examples and problems, it provides a treasure-trove of methods to construct and compute Green’s functions.