This document introduces some basic concepts in graph theory, including: - A graph G is defined as a pair (V,E) where V is the set of vertices and E is the set of edges. - Edges connect pairs of vertices and can be directed or undirected. Special types of edges include parallel edges and loops. - Special graphs include simple graphs without parallel edges/loops, weighted graphs with numerical edge weights, and complete graphs where all vertex pairs are connected. - Graphs can be represented by adjacency matrices and incidence matrices showing vertex-edge connections. - Paths and cycles traverse vertices and edges, with Euler cycles passing through every edge once.