  We describe in detail and extend a recently introduced nonperturbative
renormalization group (RG) method for surface growth. The scale invariant
dynamics which is the key ingredient of the calculation is obtained as the
fixed point of a RG transformation relating the representation of the
microscopic process at two different coarse-grained scales. We review the RG
calculation for systems in the Kardar-Parisi-Zhang universality class and
compute the roughness exponent for the strong coupling phase in dimensions from
1 to 9. Discussions of the approximations involved and possible improvements
are also presented. Moreover, very strong evidence of the absence of a finite
upper critical dimension for KPZ growth is presented. Finally, we apply the
method to the linear Edwards-Wilkinson dynamics where we reproduce the known
exact results, proving the ability of the method to capture qualitatively
different behaviors.
