This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE to structure learning, association discovery, variable selection, causal discovery, system identification, time lag estimation, domain adaptation, multivariate normality test, copula hypothesis test, two-sample test, change point detection, and symmetry test are reviewed. The relationships between the theoretical applications and their connections to correlation and causality are discussed. The framework based on CE for measuring statistical independence and conditional independence is compared to the other similar ones. The advantages of CE based methodologies over the other comparable ones are evaluated with simulations. The mathematical generalizations of CE are reviewed. The real applications of CE to every branch of science and engineering are briefly introduced.

翻译：本文是关于Copula熵（CE）理论与应用的专著。本书首先介绍了CE的理论体系，包括其背景、定义、定理、性质及估计方法。综述了CE在结构学习、关联发现、变量选择、因果发现、系统辨识、时滞估计、域适应、多元正态性检验、Copula假设检验、双样本检验、变点检测和对称性检验等理论应用方向的研究进展。探讨了这些理论应用之间的内在联系及其与相关性、因果性的关联。将基于CE的统计独立性与条件独立性度量框架与其他类似框架进行了比较，并通过仿真实验评估了基于CE的方法相较于其他可比方法的优势。回顾了CE的数学推广形式，并简要介绍了CE在科学与工程各领域的实际应用。