The paper presents a renormalization group (RNG) analysis of turbulence, aiming to understand and extend a recent theory based on RNG techniques. Yakhot and Orszag (1986) applied RNG methods to hydrodynamic turbulence, calculating an eddy viscosity consistent with the Kolmogorov inertial range by systematically eliminating small scales. Their approach assumes the smallness of nonlinear terms in the redefined equations for large scales, leading to predictions for flow constants like the Kolmogorov constant without adjustable parameters. The RNG transformation, originally developed for quantum field theories and critical phenomena, is used here to analyze turbulence. It involves eliminating small scales and rescaling space, leading to new independent variables and rescaling of dependent variables. A set of equations is renormalizable if it remains unchanged under RNG transformation, implying scale invariance. The method involves iterating the RNG transformation until convergence is achieved. New terms generated by the elimination process are classified as irrelevant, marginal, or relevant. The theory posits an equivalence between inertial range solutions of the Navier-Stokes equations and homogeneous isotropic flow driven by a Gaussian random force. The model equations are derived, with the white noise force characterized by a power law spectrum. The RNG analysis recovers the Kolmogorov spectrum when the exponent y is set to 3. A revised analysis using only scale elimination yields both scaling laws and amplitudes for the energy spectrum. Rescaling is used to justify neglect of new terms, which are marginal. The theory calculates the effect of small scales on large scales, modeling them as an eddy viscosity. The equations are expanded in a power series, with nonlinear terms approximated. The coefficient of the linear term is an integral, evaluated in the limit of small wavenumbers. Iteration of the elimination procedure leads to an equation for large scales, replacing molecular viscosity with eddy viscosity. The RNG results depend on the extrapolation of small wavenumbers and the exponent y. The nondimensionalized ordering parameter is proportional to (y+1)^{1/2}, with a fixed point value of 11.5 when y=3. A power series expansion of the energy equation at the fixed point yields the Kolmogorov constant as 1.617. The RNG method can also be applied to passive scalar advection, predicting the Batchelor constant. The paper outlines future goals, including further analysis of the RNG κ-ε model, assessing neglected terms, exploring other forcing functions, extending the theory to non-homogeneous turbulence, and testing the RNG sub-grid and κ-ε models.The paper presents a renormalization group (RNG) analysis of turbulence, aiming to understand and extend a recent theory based on RNG techniques. Yakhot and Orszag (1986) applied RNG methods to hydrodynamic turbulence, calculating an eddy viscosity consistent with the Kolmogorov inertial range by systematically eliminating small scales. Their approach assumes the smallness of nonlinear terms in the redefined equations for large scales, leading to predictions for flow constants like the Kolmogorov constant without adjustable parameters. The RNG transformation, originally developed for quantum field theories and critical phenomena, is used here to analyze turbulence. It involves eliminating small scales and rescaling space, leading to new independent variables and rescaling of dependent variables. A set of equations is renormalizable if it remains unchanged under RNG transformation, implying scale invariance. The method involves iterating the RNG transformation until convergence is achieved. New terms generated by the elimination process are classified as irrelevant, marginal, or relevant. The theory posits an equivalence between inertial range solutions of the Navier-Stokes equations and homogeneous isotropic flow driven by a Gaussian random force. The model equations are derived, with the white noise force characterized by a power law spectrum. The RNG analysis recovers the Kolmogorov spectrum when the exponent y is set to 3. A revised analysis using only scale elimination yields both scaling laws and amplitudes for the energy spectrum. Rescaling is used to justify neglect of new terms, which are marginal. The theory calculates the effect of small scales on large scales, modeling them as an eddy viscosity. The equations are expanded in a power series, with nonlinear terms approximated. The coefficient of the linear term is an integral, evaluated in the limit of small wavenumbers. Iteration of the elimination procedure leads to an equation for large scales, replacing molecular viscosity with eddy viscosity. The RNG results depend on the extrapolation of small wavenumbers and the exponent y. The nondimensionalized ordering parameter is proportional to (y+1)^{1/2}, with a fixed point value of 11.5 when y=3. A power series expansion of the energy equation at the fixed point yields the Kolmogorov constant as 1.617. The RNG method can also be applied to passive scalar advection, predicting the Batchelor constant. The paper outlines future goals, including further analysis of the RNG κ-ε model, assessing neglected terms, exploring other forcing functions, extending the theory to non-homogeneous turbulence, and testing the RNG sub-grid and κ-ε models.