Great discoveries in the history of physics have frequently been associated with study of matter under extreme conditions. The physics of small sizes requires the quantum mechanical principles while the physics of high velocities requires the special relativity. Experiments with the high energy central heavy ion collisions performed in the last decades of past century at CERN indicated closing to a new exciting threshold: onset of deconfinement and the chiral symmetry restoration in nuclear matter at high energy density. The strong interaction theory, Quantum Chromodynamics, and the lattice calculations predicted that at sufficiently high temperatures the hadronic matter will undergo transition to a state in which the quarks and gluons, usually localized inside the hadrons, become locally unbound. It results in a new extreme phase of matter, the gluon dominated Quark-Gluon Plasma (QGP), which probably was a state of the Universe in the first few microseconds following the Big Bang. On the other hand significant increase of the baryon density at comparatively low temperatures should lead to creating of the quark plasma expected to exist in the core of the neutron stars. Investigations in the laboratory conditions of these extreme new states of matter are listed in the Long-Range Plan for Nuclear Physics as the highest priority problems.

From the beginning of this century the Relativistic Heavy Ion Collider at BNL (USA) entered this new field of studies creating collisions of the gold ion beams with the energy 100 A GeV each. The principle goal of the PHENIX ,   STAR ,   PHOBOS and BRAHMS experiments at RHIC was the discovery and characterization of the QGP at high temperatures. Basing on the property of asymptotic freedom of the QCD it was expected to observe at the RHIC energies the QGP as the dense gas medium of weakly interacting quarks and gluons. During the decade of the RHIC operation a huge amount of data was accumulated and processed which opposite to the common expectation led to a conclusion that the properties of the medium created in the high energy central heavy ion collisions are more close to properties of the dense almost perfect liquid characterized by strong interaction of constituents. The detailed studies of the GQP formation are now continuing at the RHIC and at LHC in CERN where the energy of the colliding ions of lead are exceeding energy at RHIC by more than 20 times. The other limit, high baryon density but low temperature region of the phase diagram will be studied in the heavy ion collisions at FAIR and NICA facilities starting from 2016. The PNPI is active participant in almost all collaborations involved in these studies.