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The book is devoted to the discussion of modern aspects of the theory of hadronic matter under extreme conditions. It consists of 12 selected contributions to the second international workshop on this topic held in fall 2019 at JINR Dubna, Russia. Of particular value are the contributions to lattice gauge theory studies attacking the problem of simulating QCD at finite baryon densities, one of the major challenges at the present time in this field. Another unique aspect is provided by the discussion of puzzling effects that appear in the poduction of hadrons in nuclear collisions, like the horn in the K+/pi+ ratio, which are subject to hydrodynamic and reaction-kinetic modeling of these nonequilibrium phenomena.

quantum chromodynamics --- confinement --- center vortex model --- string tension --- Gribov copy problem --- chiral imbalance --- chiral perturbation theory --- linear sigma model --- charged pion decay in chiral medium --- local parity breaking --- Glauber and Giessen Boltzmann–Uehling–Uhlenbeck (GiBUU) models --- formation length --- semiexclusive processes --- ultraperipheral and central heavy ion collisions --- n,p,π and Λ+Σ0 production --- QCD phase diagram --- non-zero baryon density --- dualities --- lattice QCD --- isospin --- BCS phase --- finite density --- density of states techniques --- xenon --- heavy-ion collision --- LHC --- particle momentum spectrum --- particle number ratio --- PNJL model --- Beth–Uhlenbeck --- phase shift --- “horn” effect --- kinetic approaches to dense matter --- quark-gluon plasma --- collective flow --- nucleosynthesis --- supernova --- magnetars --- baryon density --- gluon propagator --- screening mass --- (2 + 1)-dimensional QED --- dynamical chiral symmetry breaking --- 1/N expansion --- non-local gauge

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The book edition of the Universe Special Issue “Compact Stars in the QCD Phase Diagram” is devoted to the overarching aspects shared between heavy-ion collisions and compact star astrophysics in investigating the hadron-to-quark matter phase transition in the equation of state of strongly interacting matter in different regions of the phase diagram of QCD. It comprises 22 review and research articles that, together, will serve as a useful guide in educating both young and senior scientists in this emerging field that represents an intersection of the communities of strongly interacting matter theory, heavy-ion collision physics and compact star astrophysics.

Gamma-ray bursts --- collective flow --- vector interaction --- quarks --- meson production --- ? meson condensation --- neutrino --- magnetic DCDW --- pulsars --- light cluster emission --- monte carlo simulations --- neutron stars --- chiral symmetry --- GW170817 --- stellar structure --- supernova explosions --- maximum mass --- mass-radius relation --- nuclear equation of state --- in-medium effects --- Beth-Uhlenbeck equation of state --- speed of sound --- gravitational waves --- relativistic heavy-ion collisions --- crystalline structure --- neutron star --- finite density --- transport theory --- stellar evolution --- neutron star matter --- hadronic matter --- general relativity --- critical point --- ? resonances --- QCD matter --- modified excluded-volume mechanism --- cold-dense QCD --- quark stars --- quark-hole pairing --- finite size --- mass-twin stars --- pasta phases --- hybrid stars --- cluster virial expansion --- finite temperature --- quark-hadron phase transition --- hadron–quark continuity --- stellar magnetic field --- strangeness --- quark-gluon plasma --- pulsars: PSR J0737 ? 3039A --- pulsars: general --- combustion --- Mott dissociation --- hybrid compact stars --- quark deconfinement --- quark matter --- Gravitational waves --- pulsars: PSR J1757 ? 1854 --- neutrino emissivities --- directed flow --- star oscillations --- quark-hadron matter --- QCD phase diagram --- phase transition --- equation of state --- nuclear matter --- nuclear symmetry energy --- hydrodynamics --- deconfinement --- stars: neutron --- axion QED --- Quantum Chromodynamics --- dense matter --- heavy-ion collisions