The High-Luminosity Large Hadron Collider will provide an unprecedented opportunity to study the properties of the Higgs boson and eventually probe for new physics beyond the Standard Model. The large anticipated data sample will allow for more precise investigations of topics already studied with earlier data samples, as well as for studies of processes that are accessible only with the much larger statistics. Rates and signal strengths will be measured for a variety of Higgs boson production and decay modes, allowing extraction of the Higgs boson couplings. Particular final states will allow differential cross-sections to be measured for all production modes, and for studies of the Higgs boson width and CP properties, as well as the tensor structure of its coupling to vector bosons. An important part of the High-Luminosity LHC experimental program will be investigations of the Higgs boson self-coupling, which is accessible via studies of di-Higgs production. In this note the projections of the ATLAS physics reach in the Higgs sector at the High-Luminosity LHC are discussed and some selected analyses are presented.