  We formulate the exact Wilsonian renormalization group for a system of
interacting fermions on a lattice. The flow equations for all vertices of the
Wilson effective action are expressed in form of the Polchinski equation. We
apply this method to the Hubbard model on a square lattice using both zero- and
finite- temperature methods. Truncating the effective action at the sixth term
in fermionic variables we obtain the one-loop functional renormalization
equations for the effective interaction. We find the temperature of the
instability Tc^{RG} as function of doping. We calculate furthermore the
renormalization of the angle-resolved correlation functions for the
superconductivity (SC) and for the antiferromagnetism (AF). The dominant
component of the SC correlations is of the type d while the AF fluctuations are
of the type s Following the strength of both SC and AF fluctuation along the
instability line we obtain the phase diagram. The temperature Tc^{RG} can be
identified with the crossover temperature T{co} found in the underdoped regime
of the high-temperature superconductors, while in the overdoped regime Tc^{RG}
corresponds to the superconducting critical temperature.
