Plane-wave ab initio calculations based on density function theory and the pseudopotential method have been used to investigate the structural and electronic properties of phases V, IV, III and II of ammonium nitrate (AN) crystal. The optimizations of the crystal structures have been done with full relaxation of the atomic positions and lattice parameters under the experimentally determined crystal symmetries. The periodic nature of the crystals has been considered in calculations by employing periodic boundary conditions in all three directions. For phases V, IV and II the predicted crystal structures were found in good agreement with those determined experimentally by neutron diffraction data, but for phase III the differences between the experimental and calculated values are more significant. Band structure calculations indicate that AN is an insulator with a band gap in the range 3.18-3.57 eV corresponding to its different phases. The isotropic compression of phase IV has been studied using ab initio total energy calculations in the pressure range 0-600 GPa. It has been found that over this pressure range the crystal volume is compressed by 71% of the equilibrium volume. The increase in pressure determines significant changes of the band structure, large broadening of the electronic bands together with a decrease of the band gap by about 40%. We have developed a set of intra- and intermolecular classical potentials to describe phase V of AN. These potentials are composed by pairwise Lennard-Jones, hydrogen-bonding terms and Coulombic interactions. Crystal-packing calculations performed with these potentials accurately reproduce the main crystallographic features of this phase. These potentials were further tested in isothermal-isobaric molecular dynamics simulations at atmospheric pressure. It is found that increasing the temperature does not change the translational and rotational order of the molecules inside the crystal. The thermal expansion coefficients calculated for the model indicate anisotropic behavior with large expansions along the a and b axes and a very small one along the c axis.