ABSTRACT
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5.1 Introduction The enumerative theory of planar maps is born in the early sixties with the seminal work of William T. Tutte on the enumeration of planar triangulations. Over 50 years it has led several parallel lives in combinatorics, statistical physics, quantum gravity, enumerative topology and probability theory, that have started to interact intensely only in the last ten to fifteen years. Writing a fair survey of this whole story appears to be a great challenge. We concentrate instead in this text on the combinatorial point of view on map enumeration, and only review very tangentially the physics, topology and probability literature.
