Quantum ChromoDynamics, the theory of strong nuclear force, is one of
the most remarkable theories of Nature with elegantly concise first
principles and an exceptionally broad range of phenomena to describe.
At enormous temperatures -- briefly after the Big Bang and in today's
heavy ion collision experiments, or at enormous densities -- within
compact stars, the strong force comes fully into play and determines
thermodynamic phases and transitions in such a hot and dense matter.
I shall review the recent progress in the understanding of the QCD
phase diagram, discuss open theoretical problems and outline the
strategies for discovering the features of the phase diagram in heavy
ion collision experiments.
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