SincethefirstmonographtitledEnumerativeTheoryofMapsappearedonthesubjectconsideredin1999,manyadvanceshavebeenmadebytheauthorhimselfandthosedirectedbyhimundersuchatheoreticalfoundation.
Becauseofthatbookwithmuchattentiontomapsonsurfaceofgenuszero,thismonographisinprincipleconcernedwithmapsonsurfacesofgenusnotzero.Viamaintheoreticallines,thisbookisdividedintofourpartsexceptChapter1forpreliminaries.
PartonecontainsChapters2through10.Thetheoryispresentedformapsongeneralsurfacesofgenusnotnecessarytobezero.Forthetheoryonasurfaceofgenuszeroiscomprehensivelyimprovedforinvestigatingmapsonallsurfacesofgeneranotzero.
ParttwoconsistsofonlyChapter11.Relationshipsareestablishedforbuildingupabridgebetweensupermapsandembeddingsofagraphviatheirautomorphismgroups.
PartthreeconsistsofChapters12and13.Ageneraltheoryforfindinggenusdistributionofgraphembeddings,handlepolynomialsandcrosscappolynomialsofsupermapsareconstructedonthebasisofthejointtreemethodwhichenablesustotransformaprobleminahighdimensionalspaceintoaproblemonapolygon.
Allotherchapters,i.e.,Chapters14through17,aspartfourareconcernedwithseveralaspectsofmainextensionstodistinctdirections.
Anappendixservesasatlasofsupermapsoftypicalgraphsofsmallsizeonsurfacesfortheconvenienceofreaderstochecktheirunderstanding.