In this chapter and the next we introduce some concepts and theorems from an area of graph theory known as extremal graph theory. Of the many problems encountered in this area, a common one asks for the minimum size of a graph G of a given order which guarantees that G contains a certain subgraph or possesses a certain property. More generally, an extremal problem asks for the maximum or minimum value of a graph theoretic parameter in a class of graphs with a given property.