Applying the many-body theory to quarks and gluons

The article is a brief review of three topics: (i) description of the QCD vacuum in the so-called instanton liquid approach; (ii) physics of high temperature hadronic matter; and (iii) color superconductivity in dense quark matter. More focus is on the second issue where the progress is most recent. The data from heavy ion collisions indicate robust collective flows, well described by hydrodynamics. This is in striking contradiction to expected kinetics of QGP based on weakly interacting quasiparticles, but can be explained by loosely bound q̄q and gg states leading to large rescattering. We also discuss connections to strongly coupled supersymmetric theories studied via Maldacena duality, as well as recent progress in trapped atoms with very large scattering length.