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Tutte has described in the book "Connectivity in graphs" a canonicaldecomposition of any graph into 3-connected components. In this article wetranslate (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 keyingredient we use is an extension of the so-called dissymmetry theorem, whichyields negative signs in the grammar.  As a main application we recover in a purely combinatorial way the analyticexpression found by Gim\'enez and Noy for the series counting labelled planargraphs (such an expression is crucial to do asymptotic enumeration and toobtain limit laws of various parameters on random planar graphs). Besides thegrammar, an important ingredient of our method is a recent bijectiveconstruction of planar maps by Bouttier, Di Francesco and Guitter.

A Complete Grammar for Decomposing a Family of Graphs into 3-connected Components