High density QCD

The dynamics of high partonic density QCD is presented considering, in the double logarithm approximation, the parton recombination mechanism built in the AGL formalism, developed including unitarity corrections for the nucle on as well for nucleus. It is shown that these corrections are under theore tical control. The resulting non linear evolution equation is solved in the asymptotic regime, and a comprehensive phenomenology concerning Deep Inela stic Scattering like F-2, F-L, F-2(c). partial derivativeF(2)/partial deriv ative ln Q(2), partial derivativeF(2)(A)/partial derivative ln Q(2), etc, i s presented. The connection of our formalism with the DGLAP and BFKL dynami cs, and with other perurbative (K) and non perturbative (MV-JKLW) approache s is analised in detail. The phenomena of saturation due to shadowing corre ctions and the relevance of this effect in ion physics and heavy quark prod uction is emphasized. The implications to e-RHIC, HERA-A, and LHC physics a nd some open questions are mentioned.