This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths.After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, i...