This book offers an in-depth exploration of graph theory and its core algorithms, serving as a practical reference for students, researchers, and professionals in computer science.The content spans foundational topics, including graph traversal methods such as Depth-First Search (DFS) and Breadth-First Search (BFS), alongside critical concepts like topological sorting and shortest path algorithms for directed and weighted graphs. Advanced topics include network flow techniques, such as the Ford-Fulkerson and Dinic’s algorithms, and combinatorial problems like the Traveling Salesman Problem.Readers will also gain insight into structural properties, such as bridges, articulation points, and strongly connected components, with practical applications demonstrated throughout. By focusing on clarity and precision, this book aims to bridge theory and practice in graph-based problem solving.