Graphs are a fundamental mathematical tool used to model relationships among objects. We can build a graph whenever we have a binary relation between objects. This book focuses on finite and directed graphs, which may include self-loops and parallel lines. After establishing several essential definitions, we examine one of the most crucial subgraphs: spanning trees. A spanning tree connects all vertices in the underlying connected graph with a minimum number of lines. We introduce cut-sets as a dual concept of trees; cut-sets separate a graph into two disconnected subgraphs. This chapter provides an introduction to graph theory, especially for applications in theoretical physics, specifically the Feynmann diagram and associated integral analysis.