These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...). Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhD students and researchers interested in graph theory, combinatorial probability and geometry.  Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps. weiterlesen