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Reflection groups, geometry of the discriminant and noncrossing partitions.  When W is a well-generated complex reflection group, the noncrossingpartition lattice NCP_W of type W is a very rich combinatorial object,extending the notion of noncrossing partitions of an n-gon. This structureappears in several algebraic setups (dual braid monoid, cluster algebras...).Many combinatorial properties of NCP_W are proved case-by-case, using theclassification of reflection groups. It is the case for Chapoton's formula,expressing the number of multichains of a given length in the lattice NCP_W, interms of the invariant degrees of W. This thesis work is motivated by thesearch for a geometric explanation of this formula, which could lead to auniform understanding of the connections between the combinatorics of NCP_W andthe invariant theory of W.  The starting point is to use the Lyashko-Looijenga covering (LL), based onthe geometry of the discriminant of W. In the first chapter, some topologicalconstructions of Bessis are refined, allowing to relate the fibers of LL withblock factorisations of a Coxeter element. Then we prove a transitivityproperty for the Hurwitz action of the braid group B_n on certainfactorisations. Chapter 2 is devoted to certain finite polynomial extensions,and to properties about their Jacobians and discriminants. In Chapter 3, theseresults are applied to the extension defined by the covering LL. We deduce ---with a case-free proof --- formulas for the number of submaximal factorisationsof a Coxeter element in W, in terms of the homogeneous degrees of theirreducible components of the discriminant and Jacobian for LL.

Groupes de r\'eflexion, g\'eom\'etrie du discriminant et partitions non-crois\'ees