There are two parts in the present work. The first part concerns the asymptotic set of a polynomial mapping $F: \C^n \to \C^n$. In the 90s, Zbigniew Jelonek showed that this set is a $(n-1)$ - (complex) dimensional singular variety. We gave a method, called méthode façon, for stratifying this set. We obtained a Thom-Mather stratification. Moreover, there exists a Whitney stratification such that the set of possible façons is constant on every stratum. By using the façons, we gave an algorithm for expliciting the asymptotic sets of a dominant quadratic polynomial mapping in three variables. As a result, we have a complete list of the asymptotic sets in this case. The second part concerns the set called Valette set $V_F$. In 2010, Anna and Guillaume Valette constructed a real pseudomanifold $V_F \subset \R^{2n + p}$, where $p > 0$, associated to a polynomial mapping $F: \C^n \to \C^n$. In the case $n = 2$, they proved that if $F$ is a polynomial mapping with nowhere vanishing Jacobian, then $F$ is not proper if and only if the homology (or intersection homology) of $V_F$ is not trivial in dimension 2. We gave a generalization of this result, in the case of a polynomial mapping $F = (F_1, \ldots, F_n): \C^n \to \C^n$ with nowhere vanishing Jacobian. We gave also a method for stratifying the set $V_F$. As applications, we have the stratifications of the set $K_{\infty}(F)$ of asymptotic critial values of $F$, the set $B(F)$ of bifurcation points of $F$.
