This book is devoted to the description of metamaterials, their origins and physical principles, their electromagnetic and optical properties, as well as to their potential applications. This ﬁeld has witnessed an immense gain of interest over the past few years, gathering communities as diverse as those from optics, electromagnetics, materials science, mathematics, condensed matter physics, microwave engineering, and many more. The ﬁeld of metamaterials being therefore potentially extremely vast, we have limited the scope of this book to those composite materials whose structures are substantially smaller, or at the least smaller, than the wavelength of the operating radiation. Such structured materials have been called metamaterials in order to refer to the unusual properties they exhibit, while at the same time being describable as eﬀective media and characterized by a few eﬀective medium parameters insofar as their interaction with electromagnetic radiation is concerned. We also include in this book a chapter on photonic crystals, which work on a very diﬀerent principle than metamaterials, but which have been closely connected to them and have been shown to exhibit many similar properties.