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[en] Although the Standard Model of particle physics is one of the most successful and well-tested theories in physics, many extensions to the Standard Model were proposed that aim to resolve its shortcomings. Many of these models extend the Standard Model by adding additional symmetries such as Supersymmetry with one of the simplest being the Minimal Supersymmetric Standard Model (MSSM). Supersymmetric models also require the presence of a second Higgs-doublet field which predicts the existence of additional Higgs bosons. Hence, the search for these additional Higgs bosons provides an important window into investigating physics beyond the Standard Model. In this thesis, the search for additional heavy neutral Higgs bosons A and H decaying into a fully hadronic tau lepton pair is presented based on 139 fb of data taken by the ATLAS detector during the full LHC Run-2 data taking period from 2015 to 2018. Since no significant excess of data with respect to the background estimation was found, the results are presented in terms of 95 % CL upper exclusion limits on the cross-section times branching ratio for Higgs bosons produced via gluon-gluon fusion and b-associated production. Different Higgs boson mass hypotheses are taken into account ranging from 200 GeV to 2500 GeV. A combination with the semi-leptonic search channel is performed whose exclusion limits are transformed into the m tan β parameter space of the hMSSM and various m benchmark model scenarios. The combined exclusion limit set in the hMSSM model is compared to the previous publications by the ATLAS and CMS collaboration based on early Run-2 data of 36.1 fb and 35.9 fb respectively. Compared to previous exclusion limits set by ATLAS (CMS) for the hMSSM scenario, significant improvements are observed ranging between 11 % (10 %) at m = 500 GeV up to 63 % (67 %) at m = 1200 GeV. In addition to the Higgs boson search, a novel algorithm is presented to identify and select charged particle tracks reconstructed in the ATLAS inner detector originating from hadronic tau lepton decays. The identification of these tracks is an important part of the tau lepton reconstruction and identification at ATLAS and provides information about the decay multiplicity and charge of the tau lepton. By deploying state-of-the-art recurrent neural networks the reconstruction efficiency for tau leptons with a true decay multiplicity of 1 and 3 charged hadrons improves by about 10 % and 20 % respectively. With this improvement, the neural networks achieve a reconstruction efficiency close to the maximum efficiency possible. By exploiting the flexibility of the neural networks, they can be optimized for both offline data analysis and fast software trigger applications.