Nuclear astrophysics is essential to microphysics for the complex hydrodynamics simulation of numerical supernovae explosions and neutron star merger calcu- lations. Because many aspects of equation of state (hereafter, EOS) including symmetry and thermal properties are uncertain and not well constrained by ex- periments, it is important to develop EOS with easily adjustable parameters. The purpose of this thesis is to develop the nuclear matter theory and an EOS code for hot dense matter. This thesis has two major parts. In the first part, we develop a Finite-Range Thomas Fermi (hereafter, FRTF) model for supernovae and neutron star matter based on the nuclear model of Seyler and Blanchard, and Myers and Swiatecki. The nuclear model is extended to finite temperature and a Wigner-Seitz geometry to model dense matter. We also extend the model to include additional density dependent interactions to better fit known nuclear incompressibilities, pure neutron matter, and the nuclear optical potential. Using our model, we evaluate nuclear surface properties using a semi-infinite interface. The coexistence curve of nuclear matter for two-phase equilibrium is calculated. Furthermore we calculate energy, radii, and surface thickness of closed shell nuclei in which the spin-orbit interactions can be neglected. To get an optimized parameter set for FRTF, we explore the allowed ranges of symmetry energy and the density derivative of symmetry energy. We summarize recent ex- perimental results, astrophysical inference, and theoretical pure neutron matter calculations. The correlation between symmetry energy and the surface symme- try energy in liquid droplet model is also obtained. The beta equilibrium matter is used to model the neutron star crust. The second part of the thesis is devoted to construction of a code to compute the nuclear EOS for hot dense matter that would be distributed to astrophysics community. With this code, users will be able to generate tables with adjustable parameters describing the symmetry, incompressibility, and thermal properties of nuclear matter. We use the liquid droplet approach to generate thermody- namically consistent nuclear EOS. table. Compared to previous attempts, we include neutron skin, Coulumb diffusion, and Coulomb exchange. In addition, we compute the surface tension as a function of proton fraction and temperature consistently with the bulk energy. For comparison, we generate an EOS table using the SLy4 non-relativistic Skyrme force model. For both FRTF and SLy4, more than 10 % of entries of EOS tables consists of nuclei, alpha particles, and nucleons.