  Tutte has described in the book "Connectivity in graphs" a canonical
decomposition of any graph into 3-connected components. In this article we
translate (using the language of symbolic combinatorics)
  Tutte's decomposition into a general grammar expressing any family of graphs
(with some stability conditions) in terms of the 3-connected subfamily. A key
ingredient we use is an extension of the so-called dissymmetry theorem, which
yields negative signs in the grammar.
  As a main application we recover in a purely combinatorial way the analytic
expression found by Gim\'enez and Noy for the series counting labelled planar
graphs (such an expression is crucial to do asymptotic enumeration and to
obtain limit laws of various parameters on random planar graphs). Besides the
grammar, an important ingredient of our method is a recent bijective
construction of planar maps by Bouttier, Di Francesco and Guitter.
