Measurement of Higgs couplings to top quarks and $\tau$ leptons with the ATLAS detector

Since the discovery of the Higgs boson in 2012 during the first run of the Large Hadron Collider (LHC) at CERN, extensive measurements have been performed to characterize its properties. Its mass, spin, parity and couplings have been studied in detail with no significant deviations from the SM predictions observed. The second run of the LHC saw incredible progress with the addition of new measurements. This thesis highlights the measurements of Higgs couplings to third generation fermions, first with the observation of the $t\bar t H$ process and then through improved $pp \rightarrow H \rightarrow \tau\tau$ cross section measurements. The search for the $t\bar t H$ process is discussed in the context of the $t\bar t H\rightarrow \text{multilepton}$ analysis, with an emphasis on final states with $\tau_\text{had-vis}$. A $t\bar t H$ cross section measurement, obtained in combination with results from $t\bar t (H \rightarrow \gamma \gamma)$, $t\bar t (H \rightarrow ZZ^* \rightarrow 4\ell)$ and $t\bar t (H \rightarrow b\bar{b})$, is also presented. All results are found to be compatible with the Standard Model predictions. The study of Higgs decays involving $\tau$ leptons is expanded upon with the measurement of the $pp \rightarrow H \rightarrow \tau\tau$ cross section using the full Run 2 dataset, and a new method to estimate the largest background to this measurement is introduced. The improvement in the precision of $pp \rightarrow H \rightarrow \tau\tau$ measurements coupled with an increased sensitivity to broader regions of phase space allows for a deeper scrutiny of the Standard Model predictions, with the theory still providing an accurate description of the experimental results.