Higgs Pair Production Searches with the ATLAS Experiment at the LHC and the HL-LHC

Exploring the Higgs potential and electroweak symmetry breaking is one of the main goals at the Large Hadron Collider (LHC). Higgs pair production (HH) provides experimental access to the shape of Higgs potential and is the only direct probe of the Higgs self-coupling in proton-proton collisions. This thesis presents a search for HH production in the bb$\gamma\gamma$ channel with the ATLAS experiment at the LHC with 139/fb of data at 13 TeV. The results from this search are combined with results from the bb$\tau\tau$ and bbbb channels to produce the most stringent limits on Standard Model HH production and the Higgs self-coupling to date. In addition to the present results, this thesis discuss ways to improve sensitivity to HH production during Run 3 and our projected sensitivity to HH production at the High Luminosity-LHC with 4000/fb at 14 TeV. The ATLAS Inner Tracker detector upgrade which is required to enable these searches is also presented.