We present a comprehensive first-principles investigation of all symmetrically inequivalent low-index surfaces of $\beta$-Ga${}_2$O${}_3$, examining their structural properties and thermodynamic stability across experimentally relevant growth conditions. Using density-functional theory with both the semi-local functional PBEsol and a modified PBE0 hybrid functional with 26% exact exchange, denoted PBE0(0.26), we calculate surface free energies for the (010), (100), (001), (${2}$01),(110),(111),and(11${1}$)orientations,includingtheeffectsofharmonicvibrationalcontributionsandvaryingoxygenchemicalpotentials.Wedemonstratethattheenergeticorderingremainsconsistentacrosscomputationalapproachesandthatthevibrationalcontributionsremainbelow0.2J/m$^2$ up to temperatures of 1000 K. A coordination-based model that correlates surface stability with the density of under-coordinated atoms reveals that under-coordinated oxygen atoms and tetrahedral Ga sites substantially destabilize surfaces, while exposed under-coordinated octahedral Ga atoms serve as indicators of surface stability. Our thermodynamic analysis shows that stoichiometric terminations dominate over nearly the entire range of chemical potentials relevant for $\beta$-Ga${}_2$O${}_3$ stability, while non-stoichiometric terminations emerge only under extreme reducing or oxidizing conditions. Notably, we predict the formation of stable Ga-rich terminations resembling Ga adlayers for the (100) and (${2}$01) surfaces under highly reducing conditions.