This monograph is for theoty and its extensions related to census of maps on general surfaces established on the basis of what has been done on the surface of genus zero.In spite of a number of improved results with maps on a surface of genus zero for surfaces of genus not zero. two new theoretical lines wia exploiting the relationship between super maps and embeddings of a graph on surfaces and via the joint tree technique are investigated for a variety of topics such as those in the determination of handle and crosscap polynomials of maps, genus distribution of embeddings, and others related. In particular, an appendix serves as the exhaustive counting super maps (rooted and nonrooted) including these polynomials with under graphs of small size for the reader's digests.
Although the book is mainly for researchers in mathematics, theoretical physics, chemistry, biology and others related, the basic part in each chapter can also be chosen for graduates and college teachers as references.