Erbium oxide (Er2O3) is a rare earth sesquioxide with possible applications in CMOS as a gate dielectric, in photovoltaics, and in scalable optical quantum computing technology. Further, erbium exhibits photoluminescence in the telecom C band at 1540 nm, whose fine structure depends on the crystal structure. Crystal field symmetry of the erbium site in Er2O3 governs the Stark-split states and phonon-assisted excitations in Er3+. The ground state of Er2O3 is a cubic (bixbyite) phase, but it undergoes a phase transition to monoclinic and hexagonal phases at high temperatures and pressures. In this work, we explore the electronic structure, formation energy, phonon dispersion, and Raman scattering in the three phases of Er2O3 using density functional theory. We then investigate temperature- and pressure-induced phase transitions between the three phases of Er2O3. We compare our results with existing experiments and find good agreement.