Scale invariant dynamics of surface growth

We describe in detail and extend a recently introduced nonperturbative reno rmalization group (RG) method for surface growth. The scale invariant dynam ics which is the key ingredient of the calculation is obtained as the fixed point of a RG transformation relating the representation of the microscopi c process at two different coarse-grained scales. We review the RG calculat ion for systems in the Kardar-Patisi-Zhang (KPZ) universality class and com pute the roughness exponent for the strong coupling phase in dimensions fro m I to 9. Discussions of the approximations involved and possible improveme nts are also presented. Moreover, very strong evidence of the absence of a finite upper critical dimension for KPZ growth is presented. Finally, we ap ply the method to the linear Edwards-Wilkinson dynamics where we reproduce the known exact results, proving the ability of the method to capture quali tatively different behaviors. [S1063-651X(99)07606-0].