This lecture covers the basics of graph theory, including the definition of a graph as a set of vertices and edges, different types of graphs like undirected and directed graphs, and methods for representing graphs such as adjacency lists and matrices. It also delves into traversal algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS), explaining their definitions, implementations, and runtime analysis. The lecture concludes with insights on BFS not reaching all vertices and the concept of timestamps in DFS.