This book provides a concise introduction to exponential families.Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference.Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features.With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples.The material is widely self-contained and written in a mathematical setting.It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.