The aim of this lecture is to present the notion of relation. It is elementary but important and commonly used in science and practice. Relation is a kind of interdependence between the elements of a set, but formally, it is a subset of a Cartesian product of sets. Thus we shall start this lecture with the definition and properties of Cartesian product. Then we will talk about binary relations of different types, introduce the operations on relations and we will discuss how to represent them. Separate section will be devoted to the graphs, which can be considered as a graphic illustration of relation. Graph is a very important notion in computer science. Graphs are often used to model real situations, they help to understand algorithms and serve as a particularly useful and efficient data structures. Last of all, we present the notion of many-argument relation, that is the basic notion in the relational data bases.

The notions of equivalence relation and orderings will be presented in separate lectures (see lecture 4 and 5).