  Terbium gallium garnet (TGG), Tb$_3$Ga$_5$O$_{12}$, is well known for its
applications in laser optics, but also exhibits complex low-temperature
magnetism that is not yet fully understood. Its low-temperature magnetic order
is determined by means of time-of-flight neutron powder diffraction. It is
found to be a multiaxial antiferromagnet with magnetic Tb$^{3+}$ ions forming
six sublattices of magnetic moments aligned parallel and anti-parallel to the
$\langle100\rangle$ crystallographic directions of the cubic unit cell. The
structure displays strong easy-axis anisotropy with respect to a two-fold axis
of symmetry in the local orthorhombic environment of the Tb$^{3+}$ sites. The
crystal-field splitting within the single-ion ground-state manifold is
investigated by inelastic neutron scattering on powder samples. A strong
temperature dependence of the quasidoublet ground-state is observed and revised
parameters of the crystal-field Hamiltonian are given. The results of bulk
magnetic susceptibility and magnetisation measurements are in good agreement
with values based on the crystal-field model down to 20~K, where the onset of
magnetic correlations is observed.
