Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - 'Surveys' contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - 'Contributions' collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.