Search for rare and lepton-flavor violating decays of the Higgs boson with the ATLAS detector

The Standard Model predicts several rare Higgs boson decay channels, which have not yet been observed, but that could be enhanced in theories beyond the Standard Model. Among these are decays to light leptons, e.g. \mbox{$H \to \mu \mu$}. In addition, theories beyond the Standard Model may predict lepton-flavor violating decays of the Higgs boson. Results for these searches based on $pp$ collision data collected at \mbox{\SI{13}{\TeV}} will be presented.