This book provides a thorough introduction to the fundamental principles and cutting-edge applications of metamaterials. It offers a balanced perspective, combining theoretical, experimental, and computational approaches. Topics covered include rapidly evolving areas such as metasurfaces, quantum metamaterials, and nonlinear metamaterials. The book also extends its scope beyond optics to explore applications in acoustics, thermal science, mechanics, and even seismology. A dedicated chapter discusses topological insulators, providing detailed insights into this advanced topic. The text is designed for advanced graduate students and early career researchers in the field of metamaterials. Specialists in the field will also benefit from the books presentation of new developments and innovative approaches. Two chapters focus on advanced mathematical methods, including fiber bundles, Chern numbers, pseudodifferential operators, and scattering theory. These sections are crafted to be reasonably self-contained, with references provided for readers who wish to explore these topics further.