AlPO4 belongs to the berlinite quartz type family and is a ternary wide band gap semiconductor. The structure of AlPO4 is hexagonal with space group 152 (P3(1)21). In this study, using density functional theory (DFT), we have investigated the bulk physical properties (structural, electronic band structure, elastic properties, thermal properties, optical properties and bonding features) of AlPO4 compound. The optimized structural parameters are very close to previous experimental and theoretical results. The elastic constants indicate that AlPO4 is mechanically stable and brittle in nature. The compound is moderately hard and possesses a low machinability index (mu(M) = 0.54). AlPO4 contains significant mechanical anisotropy. A positive value of tetragonal shear modulus indicates the dynamical stability of this crystal. The charge density distribution, bond population analysis, Vickers hardness, thermo-mechanical and optical properties have been investigated theoretically for the first time. The values of Pugh's ratio and Poisson's ratio revealed the brittleness of the compounds associated with strong directional covalent bonds with a mixture of ionic contributions. From the bond population analysis the bonding character is also found to be mixed with ionic and covalent characters. The thermal conductivity of the compound is low (similar to 0.54 W/m.K at high temperatures). The electronic band structure calculations reveal clear insulating behavior with a band gap of similar to 6.0 eV. Band structure calculations were carried out without and with spin-orbit coupling (SOC) to explore possible topological signature. The energy dependent optical properties conform to the electronic band structure calculations. Major optical properties like dielectric functions, refractive index, photoconductivity, absorption coefficient, loss function and reflectivity are calculated and discussed in detail in this study. The optical anisotropy of AlPO4 is quite low. It is an efficient absorber of the ultraviolet light. In contrast, in the visible region, the reflectivity is very low (similar to 4 %). Possible sectors of applications of AlPO4 have been explored.