  This is a work in progress, far from being in its final form whose purpose is
to investigate thoroughly the structure of Berkovich analytic curves and its
relation with the semi-stable reduction theorem (of which a new proof is given
here, starting from the local study of Berkovich curves) through the formalism
of "triangulations". It has been already on the author's webpage for years, but
it seems better to make it available on a public preprint server.
