chapter 1 Introduction -- chapter 2 Surfaces and maps -- chapter 3 The axiomatization and the encoding of maps -- chapter 4 Generating series and conjectures -- chapter 5 Maps in Orientable Surfaces -- chapter 6 Maps in Nonorientable Surfaces -- chapter 7 Face Regular Maps and Hypermaps -- chapter 8 Associated Graphs and their Maps -- chapter 9 Numbers of Rooted Maps -- chapter 10 Numbers of Unrooted maps -- chapter 11 Nonrealizable pairs of partitions -- chapter 12 Map Polynomials.