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The Standard Model of particle physics describes the interactions of elementary particles and the structure of matter. Most processes of the microcosm can be successfully explained with it. However, there are unexplained phenomena indicating that the Standard Model is not complete. Often a theoretical solution lies in extending the Standard Model by additional gauge bosons. These gauge bosons could manifest themselves amongst others through a decay into a lepton and an antilepton. Hence, investigating the invariant mass spectrum of these lepton-antilepton pairs could lead to the observation of a new resonance. The potential gauge bosons are neutral, could have a mass in the TeV range and are called $Z^{\prime}$ bosons. This thesis focuses on the search for such new resonances using specific theoretical models as well as a model-independent approach. The underlying data for this search has been produced in proton-proton collisions at the Large Hadron Collider at a center of mass energy of $\sqrt{s}=13$ TeV. The data has been recorded by the ATLAS detector and corresponds to an integrated luminosity of 36.1 fb$^{-1}$. The backgrounds for a possible resonance in the lepton-antilepton final states have been estimated with Monte-Carlo simulations as well as data-driven methods. Statistical tools have been used to evaluate possible discrepancies between the invariant mass spectrum in data and the estimated backgrounds. No significant deviation from the Standard Model prediction has been found. A lower limit of 4.35 TeV on the $Z^{\prime}$ boson mass has been extracted assuming a sequential Standard Model with a credibility interval of 95 %. Assuming $E_6$-motivated models lower limits from 3.80 to 4.06 TeV on the $Z^{\prime}$ boson mass have been extracted with a credibility interval of 95 %. With a model-independent approach upper limits on the production cross section multiplied with the branching ratio for decays in lepton-antilepton pairs of $Z^{\prime}$ bosons have been extracted within a restricted phase space. This enables theorists to reinterpret lepton-antilepton final states within other specific theoretical models with potentially different decay widths. Finally a search for new exotic resonances which might be hidden in the inclusive lepton-antilepton spectrum has been performed. To uncover such potential resonances the inclusive spectrum of lepton-antilepton pairs has been investigated when additional jets are present. No significant deviations from the Standard Model expectation were discovered.