This book provides a survey of linear programming in semi-infinite and infinite-dimensional spaces. It includes a treatment of duality theory and of the fundamental theory of simplex-like algorithms for linear programs posed over vector spaces which may be infinite-dimensional. However, more than half the book is devoted to a detailed investigation of various types of infinite-dimensional linear program which occur, for example, in approximation theory, optimal control theory, dynamic networks, mass transfer problems and structural design. The approach is inductive; specific problems and algorithms are discussed in detail and the authors proceed from these to more general concepts and results. The book is clearly written and is intended to be accessible to a wide audience. Numerous concrete examples are discussed, drawn from a variety of fields. Detailed numerical analysis is not included, but considerable attention is given to algorithms for the solution of infinite-dimensional linear programs.