  In this paper we attempt to give a systematic account on privileged
coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot
manifold it is meant a manifold with a distinguished filtration of subbundles
of the tangent bundle which is compatible with the Lie bracket of vector
fields. This paper lies down the background for its sequel by clarifying a few
points on privileged coordinates and the nilpotent approximation of Carnot
manifolds. In particular, we give a description of all the systems of
privileged coordinates at a given point. We also give an algebraic
characterization of all nilpotent groups that appear as the nilpotent
approximation at a given point. In fact, given a nilpotent group $G$ satisfying
this algebraic characterization, we exhibit all the changes of variables that
transform a given system of privileged coordinates into another system of
privileged coordinates in which the nilpotent approximation is given by $G$.
