This paper gives a first principles formulation of a renormalization g
roup (RG) method appropriate to study of turbulence in incompressible
fluids governed by Navier-Stokes equations. The present method is a mo
mentum-shell RG of Kadanoff-Wilson type based upon the Martin-Siggia-R
ose (MSR) field-theory formulation of stochastic dynamics. A simple se
t of diagrammatic rules are developed which are exact within perturbat
ion theory (unlike the well-known Ma-Mazenko prescriptions). It is als
o shown that the claim of Yakhot and Orszag (1986) is false that highe
r-order terms are irrelevant in the epsilon expansion RG for randomly
forced Navier-Stokes (RFNS) with power-law force spectrum ($) over cap
F(k)=D(0)k(-d+(4-epsilon)). In fact, as a consequence of Galilei cova
riance, there are an infinite number of higher-order nonlinear terms m
arginal by power counting in the RG analysis of the power-law RFNS, ev
en when epsilon much less than 4. The difficulty does not occur in the
Forster-Nelson-Stephen (FNS) RG analysis of thermal fluctuations in a
n equilibrium NS fluid, which justifies a linear regression law for d>
2. On the other hand, the problem occurs also at the nontrivial fixed
point in the FNS Model A, or its Burgers analog, when d<2. The margina
l terms can still be present at the strong-coupling fixed point in tru
e NS turbulence. If so, infinitely many fixed points may exist in turb
ulence and be associated to a somewhat surprising phenomenon: nonunive
rsality of the inertial-range scaling laws depending upon the dissipat
ion-range dynamics.