This monograph is a detailed introduction to the nascent and ever-evolving fields of metamaterials and nanophotonics, with key techniques and applications needed for a comprehensive understanding of these fields all detailed. These include the 'standard' and high-accuracy 'nonstandard' FDTD techniques, finite-difference frequency-domain mode solvers, the transfer matrix method, analytic calculations for dielectric and plasmonic waveguides, dispersion, Maxwell-Bloch and density functional theory, as well as design methods for constructing metamaterials and nanolasers, and quantum plasmonics. The book is intended for final-year undergraduates, as well as postgraduates or active researchers who wish to understand and enter these fields in a 'user-friendly' manner, and who have a basic understanding of and familiarity with electromagnetic theory.