This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.

Fabrizio Durante is a professor in the Faculty of Economics and Management at the Free University of Bozen-Bolzano. He is an associate editor of Computational Statistics & Data Analysis and Dependence Modeling. His research focuses on multivariate dependence models with copulas, reliability theory and survival analysis, and quantitative risk management. He earned a PhD in mathematics from the University of Lecce and habilitation in mathematics from the Johannes Kepler University Linz.

Carlo Sempi is a professor in the Department of Mathematics and Physics at the University of Salento. He has published nearly 100 articles in many journals. His research interests include copulas, quasi-copulas, semi-copulas, weak convergence, metric spaces, and normed spaces. He earned a PhD in applied mathematics from the University of Waterloo.

Copulas: Basic Definitions and Properties. Copulas and Stochastic Dependence. Copulas and Measures. Copulas and Approximation. The Markov Product of Copulas. A Compendium of Families of Copulas. Generalizations of Copulas: Quasi-Copulas. Generalizations of Copulas: Semi-Copulas. Bibliography. Index.