In 1736, Euler founded Graph Theory by solving the Konigsberg seven-bridge problem. It has been more than two hundred years till now. Graph Theory is the core content of Discrete Mathematics, and Discrete Mathematics is the theoretical basis of Computer Science and Network Information Science. This book vulgarly introduces in an elementary way some basic knowledge and the primary methods in Graph Theory. Through some interesting mathematic problems and games the authors expand the knowledge of Middle School Students and improve their skills in analyzing problems and solving problems.