  The main purpose of this article is to classify contact structures on some
3-manifolds, namely lens spaces, most torus bundles over a circle, the solid
torus, and the thickened torus T^2 x [0,1]. This classification completes
earlier work (by Etnyre [math.DG/9812065], Eliashberg, Kanda, Makar-Limanov,
and the author) and results from the combination of two techniques: surgery,
which produces many contact structures, and tomography, which allows one to
analyse a contact structure given a priori and to create from it a
combinatorial image. The surgery methods are based on a theorem of Y.
Eliashberg -- revisited by R. Gompf [math.GT/9803019] -- and produces
holomorphically fillable contact structures on closed manifolds. Tomography
theory, developed in parts 2 and 3, draws on notions introduced by the author
and yields a small number of possible models for contact structures on each of
the manifolds listed above.
