  The wide band gap semiconductor \b{eta}-Ga2O3 shows promise for applications
in high-power and high-temperature electronics. The phonons of \b{eta}-Ga2O3
play a crucial role in determining its important material characteristics for
these applications such as its thermal transport, carrier mobility, and
breakdown voltage. In this work, we apply predictive calculations based on
density functional theory and density functional perturbation theory to
understand the vibrational properties, phonon-phonon interactions, and
electron-phonon coupling of \b{eta}-Ga2O3. We calculate the directionally
dependent phonon dispersion, including the effects of LO-TO splitting and
isotope substitution, and quantify the frequencies of the infrared and
Raman-active modes, the sound velocities, and the heat capacity of the
material. Our calculated optical-mode Gr\"uneisen parameters reflect the
anharmonicity of the monoclinic crystal structure of \b{eta}-Ga2O3 and help
explain its low thermal conductivity. We also evaluate the electron-phonon
coupling matrix elements for the lowest conduction band to determine the phonon
mode that limits the mobility at room temperature, which we identified as a
polar-optical mode with a phonon energy of 29 meV. We further apply these
matrix elements to estimate the breakdown field of \b{eta}-Ga2O3. Our
theoretical characterization of the vibrational properties of \b{eta}-Ga2O3
highlights its viability for high-power electronic applications and provides a
path for experimental development of materials for improved performance in
devices.
