The nucleus-nucleus collisions at relativistic and ultrarelativistic energies offer a unique opportunity to obtain high excited and dense nuclear matter. A number of phase transitions, from normal nuclear matter to the quark-gluon plasma, are possible in such matter. The formation of the quark-gluon plasma in these conditions can be discussed in the terms of the cosmological scenarios on the formation and evolution of the Universe. The present work presents a few new experimental results, as well as a few simulation results on the behaviour of high excited and dense nuclear matter formed in such collisions. The experimental results, as well as the simulation codes predictions, are obtained in the framework of a few international collaborations where the team members from the Nuclear Matter in Extreme Conditions Research Center are involved, namely: SKM 200, MARUSYA at JINR Dubna (Russia), BRAHMS at RHIC-BNL (USA) and CBM-FAIR at GSI Darmstadt (Germany).