Introduction to Photonic and Phononic Crystals and Metamaterials, by Arthur R. McGurn, presents a study of the fundamental properties of optical and acoustic materials which have been of recent interest in nanoscience and device technology. The level of the presentations is appropriate for advanced undergraduates, beginning graduate students, and researchers not directly involved in the field. References are given to guide the reader to more advanced study in these fields. Discussions of the physics of photonic and phononic crystals focus on the transmission properties of optical and acoustic radiation arising from their diffractive interaction in these engineered materials. The frequency transmission and non-transmission bands of radiation are explained in terms of the symmetry properties of the photonic and phononic artificial crystal structures. Basic applications of these properties to a variety of their technological applications are examined. The physics of metamaterials is discussed along with their relationships to the ideas of resonance. Properties of negative index of refraction, perfect lens, and unusual optical effects the new optics of metamaterial media makes available are examined. Related effects in acoustics are also covered. Basic principles of surface acoustic and electromagnetic waves are explained. These form an introduction to the fundamental ideas of the recently developing fields of plasmonics and surface acoustics.