Let $S$ be a finite and locally free $R$-algebra, and let $\mathrm {norm}: S \to R$ be the usual norm map. We construct a functor $N: S\text {-}\mathbf {Mod} \to R\text {-}\mathbf {Mod} $ which extends both the “Corestriction” introduced by C. Riehm when $S/R $ is a finite separable fields extension, and its generalisation by Knus and Ojanguren in case where $S$ is étale over $R$. Unlike these, the definition we give does not rely upon descent methods, but it rather uses a universal property : $N(F)$ is equipped with a $R$-polynomial law $\nu _F : F \to N(F)$ satisfying the relations $\nu _F(sx) = \mathrm {norm}(s)\nu _F(x)$, for $s \in S$ and $x \in F$, and the couple $(N(F), \nu _F)$ is universal for these properties. We thus get a well defined functor even if $S$ is ramified over $R$, but then the image of a projective $S$-module may fail to be projective over $R$. Nevertheless, the norm of an invertible $S$-module is always invertible and for these modules our construction gives the ical one. Moreover, if $S$ is locally of the form $R[X] / (P)$, then $N(F)$ is projective over $R$ for any projective $S$-module (of finite type) ; but that fails to be true if $R \to S$ is only supposed to be a complete intersection morphism. These points are discussed in some details before we focus on the étale case in order to emphasize the isomorphism between the “Weil restriction” and the norm functor (when applied to commutative algebras), and the intricate relations between $N(S\otimes E)$ and $E^{\otimes d}$ for a $R$-module $E$.