Today, quarks are considered to be elementary particles in the standard model.
Quarks seem to always form hadrons such as protons or neutrons. This phenomenon is known as confinement and is not well understood.
Quantum Chromodynamics (QCD), our theory for strong interaction, predicts that a phase transition occurs between hadronic matter and a quark and gluon plasma at around 200 MeV. At a sufficiently high energy, the coupling constant is small enough to allow perturbative expansion but the processes involved in the phase transition are of low energy.
The Nambu Jona-Lasinio (NJL) model can be seen as a low energy version of QCD where quarks are the only degrees of freedom. The Lagrangian of this model is constructed such that the symmetries of QCD that are also observed in nature are part of it. Recently, Polyakov loop has been added to try to reproduce the gluons effect as a mean field.
I will introduce you the symmetries of QCD, how the NJL model can be obtained and how one can construct hadrons from it.