ABSTRACT
In this chapter we introduce the definitions and properties that constitute the essentials of copula theory. After introducing the relevant notations (Section 1.1), in Section 1.2 we recall the bare minimum that is necessary in order to understand the meaning and the use of random variables and distribution functions, and introduce those concepts that are appropriate when studying their connexion with copulas. The remaining sections are devoted to the study of basic definitions and properties of copulas from both a probabilistic and an analytic point of view.
