A search for the production of a Higgs boson in association with a single top quark (tHq) in multilepton final states is presented in this thesis. Two different final states are studied in this work: three leptons and two leptons with same electric charge, being these leptons either electrons or muons. The results are based on an exhaustive analysis of the proton-proton collision data recorded by the ATLAS experiment at the LHC at a centre-of-mass energy of 13 TeV. As for today, this is the only analysis sensitive to both the magnitude and the sign of the Yukawa coupling of the Higgs boson to the top quark (yt(SM)) and the first direct search of tHq production in the ATLAS collaboration. In the Standard Model of Particles Physics, the tHq signal process has a predicted extremely low production cross-section (~70 fb at 13 TeV), which originates from the destructive interaction of the Feynman diagrams where the Higgs boson couples to the top quark with those where the Higgs boson couples to the W boson. If Charge-Parity (CP) is not conserved, the production cross-section could increase up to an order of magnitude in case of complete CP violation Search for associated production of a Higgs boson and a single top quark in the multi-lepton final state with ATLAS (yt = -yt(SM)). The Standard Model processes giving rise to similar final states have production cross-sections up to seven times higher and constitute the backgrounds of the tHq signal process. This fact makes multivariate-analysis methods a key tool. The implemented multivariate analyses are based on several boosted decision trees. Their objectives are to enhance a given process against the other processes to define either the signal, control or validation regions. Thus, these regions are used to test the presence of the tHq process using a profile-likelihood-binned fit. The observed signal strength for the tHq process for the three-lepton final state is 6.2±7.1, and 5.1±4.8 for the two-leptons same-sign final state. In addition, the upper limits of the signal strength are extracted using the CLs method at a 95% confidence level. The expected (observed) upper limit is <14.2 (<20.3) for the three-leptons final state and <10.8 (<16.4) for the two-leptons same-sign final state.