The Balitsky-Kovchegov equation for dipole gluon density in the momentum space

I present derivation the BK equation for the dipole gluon density in momentum space, starting from its standard formulation in coordinate space. I review the equation for both proton and nuclear targets, and I also discuss the resummed BK evolution.The purpose of this paper is to consolidate derivations and formulas scattered across the literature, to show in detail how the structure of the triple-Pomeron vertex emerges in the unfolded form of the nonlinear term, and to establish a consistent notation throughout.