Lévy Matters IV is a specialized book that focuses on the latest advancements in statistics for discretely observed Lévy processes. In an era where the statistics of stochastic processes are gaining importance in various fields such as finance, biosciences, and telecommunications, this book offers a comprehensive analysis and well-founded insights. It consists of three chapters written by leading experts in the field. Each chapter addresses specific aspects of estimating Lévy processes, taking into account both low-frequency and high-frequency data. The authors employ innovative methods to construct adaptive estimators and tackle the challenges of parametric and non-parametric estimation. This book is a valuable resource for professionals and students engaged in the theory and application of Lévy processes.