This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen graph, Paley graphs, Hamming graphs, and the Hoffman-Singleton graph, with emphasis on their symmetry and combinatorial structure. Connections with permutation groups are also discussed. Computational examples using SageMath are included to illustrate key concepts and to compute automorphism groups and related invariants.