This volume is a self-contained and carefully worked out introduction to a very active area of contemporary research. It is aligned with the general design of the work, providing extensive discussions of applications and many exercises to accompany the text. Topics covered include applications to non-linear differential and integral equations, differential inequalities, one and multi-dimensional variational problems, linear and convex optimization problems, problems in approximation theory and game theory, continuous and discrete control problems for ordinary and partial differential equations, and several important approximation techniques.