This book is devoted to dispersion theory in linear and nonlinear optics. Dispersion relations and methods of analysis in optical spectroscopy are derived with the aid of complex analysis. The book introduces the mathematical basis and derivations of various dispersion relations that are used in optical spectroscopy. In addition, it presents the dispersion theory of the nonlinear optical processes which are essential in modern optical spectroscopy. The book includes new methods such as the maximum entropy model for wavelength-dependent spectra analysis.