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...).A “Markovian� approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface. 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.

How are our societies being transformed by internet and digital economics? This book provides an accessible introduction to the economics of the internet and a comprehensive account of the mechanisms of the digital economy. Leading scholars examine the original economic and business models being developed as a result of the internet system, and explore their impact on our economies and societies. Key issues are analysed, including the development of open source software and on-line communities, peer-to-peer and online sharing of cultural goods, electronic markets and the rise of new information intermediaries, e-retailing and e-banking. The volume examines how internet and digital economics have transformed the organization of firms, industries, markets, commerce, modes of distribution, money, finance, and innovation processes, and provides the analytical tools to understand both these recent transformations and the likely future directions of the 'New Economy'.

How are our societies being transformed by internet and digital economics? This book provides an accessible introduction to the economics of the internet and a comprehensive account of the mechanisms of the digital economy. Leading scholars examine the original economic and business models being developed as a result of the internet system, and explore their impact on our economies and societies. Key issues are analysed, including the development of open source software and on-line communities, peer-to-peer and online sharing of cultural goods, electronic markets and the rise of new information intermediaries, e-retailing and e-banking. The volume examines how internet and digital economics have transformed the organization of firms, industries, markets, commerce, modes of distribution, money, finance, and innovation processes, and provides the analytical tools to understand both these recent transformations and the likely future directions of the 'New Economy'.