Quantum Chromodynamics dictates that in extreme conditions of high temperature and high density, hadronic matter forms a new form of elementary matter: quark-gluon matter. Quark-gluon matter encompasses the hot strongly-coupled liquid known as Quark-Gluon Plasma (QGP) that filled the early universe and is produced in heavy-ion collisions. To the surprise of the broader particle physics community, quark-gluon matter signatures have been measured in high-multiplicity proton-proton and proton-lead collisions, opening up experimental inroads to study not only the properties of quark-gluon matter but also the dynamical non-equilibrium processes that lead to its formation. This program will critically assess the theoretical description of the properties and dynamics of quark-gluon matter, and identify the future challenges of the field in the next decade. In particular, we aim to bring new theoretical insights that will deepen our understanding of existing and upcoming experimental measurements. Key to this goal will be a vibrant environment that will bring together heavy-ion experts with researchers of three neighboring fields: high-energy particle physics, nuclear structure and formal theory. The program will push the boundaries of the precision frontier with emphasis on the role of out-of-equilibrium QCD, nuclear structure, global analyses, and high-energy probes and the quantum frontier, where formal theoretical developments related to conformal field theory, holography, and confinement meet our understanding of quark-gluon matter.