Textbook in PDF format The author's passion for teaching core computer science courses, particularly discrete math and algorithms, inspired this book. Graphs are crucial in solving real-world problems, and this book aims to present graph theory gradually and accessibly. It provides a comprehensive overview of foundational and advanced concepts, starting with an introduction to graph theory, types of graphs, and their significance. The book covers key terms, properties, Eulerian and Hamiltonian graphs, isomorphism, subgraphs, and special graphs such as complete and bipartite graphs. The representation of graphs is discussed highlighting their practical applications and differences. A dedicated chapter showcases the use of graphs such as search engines, networks, and bioinformatics. Various graph algorithms are detailed, including Eulerian tours, shortest paths, minimum spanning trees, maximum flow, and matching. An appendix on algorithm complexity provides insights into analyzing algorithms, time complexity. This book is ideal for undergraduate and graduate students in mathematics, computer science, engineering, and those interested in mathematical structures. It is also valuable for software engineers and developers interested in modeling systems