The notion of a graph serves as a simple but useful mathematical model with which one can study successfully a wide variety of phenomena in the natural and social sciences. After introducing this concept, the goal of this section is to study various problems in discrete mathematics that can be expressed in the language of graph theory and to acquaint the reader with the methods of this theory. Some of these problems concern special classes of graphs (such as trees, bipartite graphs, and planar graphs), which will be studied in separate sections.