  This paper is concerned with suitable generalizations of a plane de
Jonqui\`eres map to higher dimensional space $\mathbb{P}^n$ with $n\geq 3$. For
each given point of $\mathbb{P}^n$ there is a subgroup of the entire Cremona
group of dimension $n$ consisting of such maps. One studies both geometric and
group-theoretical properties of this notion. In the case where $n=3$ one
describes an explicit set of generators of the group and gives a homological
characterization of a basic subgroup thereof.
