  The AdS/CFT transformation relates two nonlinear realizations of
(super)conformal groups: their realization in the appropriate field theories in
Minkowski space with a Goldstone dilaton field and their realization as
(super)isometry groups of AdS (super)spaces. It exists already at the classical
level and maps the field variables and space-time coordinates of the given
(super)conformal field theory in $d$-dimensional Minkowski space ${\cal M}_d$
on the variables of a scalar codimension one (super)brane in AdS$_{d+1}$ in a
static gauge, the dilaton being mapped on the transverse AdS brane coordinate.
We explain the origin of this coordinate map and describe some its
implications, in particular, in $d=1$ models of conformal and superconformal
mechanics. We also give a suggestive geometric interpretation of this AdS/CFT
transform in the pure bosonic case in the framework of an extended
$2d+1$-dimensional conformal space involving extra coordinates associated with
the generators of dilatations and conformal boosts.
