Two of the most powerful tools used to study magnetic materials are inelastic neutron scattering and THz spectroscopy. Because the measured spectra provide a dynamical fingerprint of a magnetic material, these tools enable scientists to unravel the structure of complex magnetic states and to determine the microcscopic interactions that produce them. This book discusses the experimental techniques of inelastic neutron scattering and THz spectroscopy and provides the theoretical tools required to analyze their measurements using spin-wave theory. For most materials, this analysis can resolve the microscopic magnetic interactions such as exchange, anisotropy and Dzyalloshinskii–Moriya interactions. Assuming a background in elementary statistical mechanics and a familiarity with the quantized harmonic oscillator, this work presents a comprehensive review of spin-wave theory and its applications to both inelastic neutron scattering and THz spectroscopy. Spin-wave theory is used to study several model magnetic systems, including non-collinear magnets such as spirals and cycloids that are produced by geometric frustration, competing exchange interactions, or Dzyalloshinskii–Moirya interactions. Several case studies utilizing spin-wave theory to analyze inelastic neutron scattering and THz spectroscopy measurements are presented. These include both single crystals and powders, and both oxides and molecule-based magnets. In addition to sketching the numerical techniques used to fit dynamical spectra based on microscopic models, this book also contains more than 70 exercises that can be performed by beginning graduate students.