  We present an analytical method, rooted in the non-perturbative
renormalization group, that allows one to calculate the critical exponents and
the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth
equation in all its different regimes, including the strong-coupling one. We
analyze the symmetries of the KPZ problem and derive an approximation scheme
that satisfies the linearly realized ones. We implement this scheme at the
minimal order in the response field, and show that it yields a complete,
qualitatively correct phase diagram in all dimensions, with reasonable values
for the critical exponents in physical dimensions. We also compute in one
dimension the full (momentum and frequency dependent) correlation function, and
the associated universal scaling functions. We find an excellent quantitative
agreement with the exact results from Praehofer and Spohn (J. Stat. Phys. 115
(2004)). We emphasize that all these results, which can be systematically
improved, are obtained with sole input the bare action and its symmetries,
without further assumptions on the existence of scaling or on the form of the
scaling function.
