**by Polychronis Koliogiannis**

Neutron stars are the way for the Universe to manifest its densest objects with an internal structure. Their study requires the knowledge of the equation of state of the fluid in the interior of the star. While isolated neutron stars place constraints on the cold, catalysed matter, many dynamical phenomena depend sensitively on the equation of state of hot dense nuclear matter. The formation of proto-neutron stars, neutron stars mergers, as well as the aftermath remnant, depend on the equation of state at finite temperature, entropy per baryon, and a varying range of proton fraction. In this framework, we construct thermodynamically consistent equations of state to accurately describe thermal effects. Additionally, we study the thermal and rotation with the Kepler frequency effect on some of the most important quantities in neutron stars, including the mass and radius, the frequency, the Kerr parameter, the moment of inertia, etc. The extended study on these quantities and data from late observations of neutron stars, both isolated and in matter of merging, could provide useful insight and robust constraints on the equation of state of nuclear matter.