  Gromov proposed to extract the (differential) geometric content of a
sub-riemannian space exclusively from its Carnot-Carath\'eodory distance. One
of the most striking features of a regular sub-riemannian space is that it has
at any point a metric tangent space with the algebraic structure of a Carnot
group, hence a homogeneous Lie group. Siebert characterizes homogeneous Lie
groups as locally compact groups admitting a contracting and continuous
one-parameter group of automorphisms. Siebert result has not a metric
character.
  In these notes I show that sub-riemannian geometry may be described by about
12 axioms, without using any a priori given differential structure, but using
dilation structures instead. Dilation structures bring forth the other
intrinsic ingredient, namely the dilations, thus blending Gromov metric point
of view with Siebert algebraic one.
