The discovery of the Higgs boson has led to extensive research on its properties, with one of its key parameter remaining only loosely constrained: the Higgs self-interaction parameter. This parameter influences the Higgs potential, affecting the Electroweak Symmetry Breaking and the Higgs mechanism, which is responsible for generating mass for particles in the Standard Model. Di-Higgs (hh) production at the LHC provides a direct probe of the Higgs self-interaction. This thesis explores new physics affecting hh production via Effective Field Theories (EFT), enabling hh searches for new physics with minimal assumptions on the Beyond the Standard Model physics that could alter the Higgs self-interaction among other interactions. This work presents hh EFT interpretations of data from the ATLAS experiment collected during Run 2 (2015-2018), using 126-140 inverse femtobarn of proton-proton collision data with a center-of-mass energy of 13 TeV. The results include interpretations in terms of Standard Model Effective Field Theory and Higgs Effective Field Theory in the decay channels containing two b-quarks and two photons, four b-quarks and two b-quarks with two tau-leptons. All measurements are consistent with the Standard Model predictions, and limits are derived for various Wilson coefficients and EFT benchmark points.

A major focus of this thesis is the development and application of a method called `reweighting', which plays a crucial role in EFT interpretations. This method enables EFT interpretations by parameterizing the EFT signal as a function of the truth invariant mass of the di-Higgs system and the Wilson coefficients deemed relevant in hh production.

Optimization and performance studies of the ATLAS Jet-Vertex-Tagger, aimed at suppressing pile-up jets, are presented. The studies demonstrate improved suppression through modified track-to-vertex-association and multivariate algorithm training using events with Run 2 detector and beam conditions, along with particle flow jets as input.