  Two of the most striking experimental findings when investigating exciton
spectra in cuprous oxide using high-resolution spectroscopy are the
observability and the fine structure splitting of $F$ excitons reported by J.
Thewes et al. [Phys. Rev. Lett. 115, 027402 (2015)]. These findings show that
it is indispensable to account for the complex valence band structure and the
cubic symmetry of the solid in the theory of excitons. This is all the more
important for magnetoexcitons, where the external magnetic field reduces the
symmetry of the system even further. We present the theory of excitons in
$\mathrm{Cu_{2}O}$ in an external magnetic field and especially discuss the
dependence of the spectra on the direction of the external magnetic field,
which cannot be understood from a simple hydrogen-like model. Using
high-resolution spectroscopy, we also present the corresponding experimental
spectra for cuprous oxide in Faraday configuration. The theoretical results and
experimental spectra are in excellent agreement as regards not only the
energies but also the relative oscillator strengths. Furthermore, this
comparison allows for the determination of the fourth Luttinger parameter
$\kappa$ of this semiconductor.
