This book summarizes studies and major materials on data compression methods in analytical spectroscopy, including some important topics on imaging. Its rigorous mathematical basis, in-depth detailed description, and numerous examples of the applications in chemistry and physics will be of value for theorists, practitioners, and students specializing in spectroscopy, chemometrics, and analytical chemistry.This text differs from existing brief reviews and articles on this topic in that it forms, for the first time, an overview of all kinds of compression methods in spectroscopy. In addition, it provides quickly reproducible computer calculations, illustrating its significant theoretical statements. As such, it can also serve as a practical guide to lecturers in spectroscopy, chemometrics, and analytical chemistry.