This is the first one-volume work to provide a thorough and comprehensive description of the physical background, rigorous theory and applications of Kramers-Kronig relations in the fields of linear and nonlinear optical spectroscopy. Currently, Kramers-Kronig relations have become basic tools in the investigation of the optical properties of materials. A brief presentation of a related data-retrieval technique, the maximum entropy method, is also given. Computer codes for data analysis via Kramers-Kronig relations are also provided. The contents and style potentially make this a standard text for physicists, chemists and engineers interested in optical-materials research and development.