Neutron stars are formed as a result of core-collapse supernova explosions. 

To comprehend both neutron stars and these supernovae, accurate dense matter physics, 

specifically the equation of state (EOS), is essential. With the advent of multimessenger astronomy, 

we have access to extensive information on neutron stars and dense nuclear matter.

 However, since the EOS for dense matter remains uncertain, I will explain a straightforward

 yet practical method for constructing the nuclear equation of state known as the 'Energy Density Functional' (EDF). 

Additionally, I will address the speed of sound in dense nuclear matter as part of constructing the nuclear EOS. 

The EDF approach is extended to develop the hot dense matter EOS (or EOS table), which is a crucial input 

for supernova explosion simulations. Various methods for creating EOS tables will be discussed during the colloquium. 

In this talk, I will present and analyze the latest results obtained from the Liquid Drop Model (LDM) and EDF,

incorporating the most recent parameters.