This book highlights the discussions by renown researchers on questions emerged during transition from the relativistic heavy-ion collider (RHIC) to the future electron ion collider (EIC). Over the past two decades, the RHIC has provided a vast amount of data over a wide range of the center of mass energies. What are the scientific priorities, after RHIC is shut down and turned to the future EIC? What should be the future focuses of the high-energy nuclear collisions? What are thermodynamic properties of quantum chromodynamics (QCD) at large baryon density? Where is the phase boundary between quark-gluon-plasma and hadronic matter at high baryon density? How does one make connections from thermodynamics learned in high-energy nuclear collisions to astrophysical topics, to name few, the inner structure of compact stars, and perhaps more interestingly, the dynamical processes of the merging of neutron stars? While most particle physicists are interested in Dark Matter, we should focus on the issues of Visible Matter! Multiple heavy-ion accelerator complexes are under construction: NICA at JINR (4 ~ 11 GeV), FAIR at GSI (2 ~ 4.9 GeV SIS100), HIAF at IMP (2 ~ 4 GeV).  In addition, the heavy-ion collision has been actively discussed at the J-PARC. The book is a collective work of top researchers from the field where some of the above-mentioned basic questions will be addressed. We believe that answering those questions will certainly advance our understanding of the phase transition in early universe as well as its evolution that leads to today's world of nature.