  Quantum chromodynamics (QCD) at finite temperature, $T$, and quark chemical
potential, $\mu$, has a rich phase structure: at low $T$ and low $\mu$, the
Nambu-Goldstone (NG) phase with nearly massless pions is realized by the
dynamical breaking of chiral symmetry through condensation of quark-anti-quark
pairs, while, at low $T$ and high $\mu$, a Fermi liquid of deconfined quarks is
expected to appear as a consequence of asymptotic freedom. Furthermore, in such
a cold quark matter, condensation of quark-quark pairs leads to the color
superconductivity (CSC). At high $T$ for arbitrary $\mu$, all the condensates
melt away and a quark-gluon plasma (QGP) is realized. The experimental
exploration of thermal phase transition from the NG phase to QGP is being
actively pursued in ultrarelativistic heavy ion collisions at RHIC
(Relativistic Heavy Ion Collider), and will be continued in the future at LHC
(Large Hadron Collider). The quantum phase transition from the NG phase to the
CSC at low $T$ is also relevant to heavy-ion collisions at moderate energies,
and is of interest in the interiors of neutron stars and possible quark stars.
In this Chapter, after a brief introduction to the basic properties of QCD, the
current status of the QCD phase structure and associated quantum phase
transitions will be summarized with particular emphasis on the symmetry
realization of each phase. Possible connection between the physics of QCD and
that of ultracold atoms is also discussed.
