Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem — a proof that revolutionized the field of graph theory — and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.