Basic concepts and methods of graph theory. Sets and polysets, equivalence relations. Routes, tracks, paths, circles, cohesive components. Junctions and bridges. Mathematical induction on integers and structural induction. Using Structural Induction in Graph Classes. Trees and forests. Spanning trees and elementary cycles. Using structural induction on trees. Helly property. Inductive computation of tree centers. Concepts of bicoherence, bicoherent components. Menger’s theorem. Graph analysis in disjoint components. Graphs of biconnected components and their applications. Strong cohesion, strongly cohesive components.