This chapter introduces the theory of graphs, which are simple structures consisting of points ( vertices ) connected by lines ( edges ). Graph theory has broad applications, including in computer chip design, electronic circuit design, and solving puzzles and games. The chapter highlights the complexity of some graph theory problems, such as the four-color theorem, which states that only four colors are needed to color any map so that no two adjacent countries share the same color. The chapter begins by defining three types of graphs: directed graphs (digraphs), undirected graphs, and multigraphs. Directed graphs are represented with arrows to indicate the direction of edges, while undirected graphs use lines without arrows. Multigraphs allow multiple edges between the same pair of vertices. The chapter also discusses the relationship between undirected graphs and digraphs with symmetric relations, showing that they are one-to-one correspondences.This chapter introduces the theory of graphs, which are simple structures consisting of points ( vertices ) connected by lines ( edges ). Graph theory has broad applications, including in computer chip design, electronic circuit design, and solving puzzles and games. The chapter highlights the complexity of some graph theory problems, such as the four-color theorem, which states that only four colors are needed to color any map so that no two adjacent countries share the same color. The chapter begins by defining three types of graphs: directed graphs (digraphs), undirected graphs, and multigraphs. Directed graphs are represented with arrows to indicate the direction of edges, while undirected graphs use lines without arrows. Multigraphs allow multiple edges between the same pair of vertices. The chapter also discusses the relationship between undirected graphs and digraphs with symmetric relations, showing that they are one-to-one correspondences.