The Standard Model (SM) of particle physics successfully explains most of the experimental results. Yet, there are some phenomena that cannot be described by the SM, and that implies a new physics beyond the SM. Supersymmetry (SUSY) is one of the natural extensions of the SM, based on boson–fermion symmetry, which predicts existence of a supersymmetric partner for each SM particle. The Minimal Supersymmetric Standard Model (MSSM) with the R-parity conservation is expected to solve several problems in the SM. The masses of the SUSY particles depend on the parameters in the MSSM Lagrangian, which provides various scenarios with different mass spectra. Many scenarios in the MSSM favor the SUSY particles lighter than O(TeV), thus they can be probed by the experiments at the Large Hadron Collider (LHC). The naturalness argument on the Higgs boson mass supports the “Higgsino scenario”, whereas the compatibility of the SUSY particle with the dark matter motivates the “Wino/Bino scenario”. Both of the scenarios predict compressed mass spectra, where the mass of the lightest neutralino \tilde{Chi}^0_1 is close to the masses of the chargino \tilde{Chi}^{\pm}_1 and the second-to-lightest neutralino \tilde{Chi}^0_2. In those scenarios, only low-momentum particles are kinematically allowed to appear in the decay of \tilde{Chi}^0_2 / \tilde{Chi}^{\pm}_1 into \tilde{Chi}^0_1. This thesis presents results of search for electroweak production of \tilde{Chi}^{\pm}_1 , \tilde{Chi}^0_2 and \tilde{Chi}^0_1 with compressed mass spectra. The search uses 139 fb^{−1} of \sqrt{s} = 13 TeV proton--proton collision data at the LHC collected by the ATLAS detector. The search assumes pair production of SUSY particles via electroweak interactions, which decay into the lightest neutralinos \tilde{Chi}^0_1 and SM particles. The lightest neutralinos are invisible in the detector, thus are observed as missing momentum in the transverse direction. The decay process \tilde{Chi}^0_2 \to Z^* \tilde{Chi}^0_1 followed by Z \to ll leads to a characteristic kinematic edge in the spectrum of the invariant mass of the two leptons, at ∆m = m(\tilde{Chi}^0_2) − m(\tilde{Chi}^0_1). The search exploits this feature, using events with two leptons that form a small invariant mass. Events with missing transverse momentum and two same-flavor, oppositely charged leptons are selected, with presence of hadronic activity from initial-state radiation. The compressed mass spectrum expected in the Higgsino and the Wino/Bino scenarios leads to small transverse momentum (pT) of the two leptons. Various new techniques to efficiently reconstruct low-pT leptons, as well as data-driven methods to estimate the backgrounds are applied in the search to enhance the sensitivity for the compressed scenarios. Finally no signals from the MSSM are observed in this search. The data are consistent with predictions from the SM, and the 95% C.L. exclusion limits on the mass of the second-to-lightest neutralino m(\tilde{Chi}^0_2) are set as functions of the mass difference ∆m = m(\tilde{Chi}^0_2) − m(\tilde{Chi}^0_1), for the Higgsino and the Wino/Bino scenarios. For the Higgsino scenario, the lower limits on m(\tilde{Chi}^0_2) is set at 193 GeV for \Delta m = 9.3 GeV, and 92.4 GeV for \Delta m = 2.3 GeV. For the Wino/Bino scenario, two different parameters that produce the same mass spectra are considered. In the first parameter set, the lower limits on m(\tilde{Chi}^0_2) is set at 240 GeV for \Delta m = 7.0 GeV and 92.4 GeV for \Delta m = 1.5 GeV. In the second parameter set, the lower limits on m(\tilde{Chi}^0_2) is set at 241 GeV for \Delta m = 9.0 GeV and 92.4 GeV for \Delta m = 1.7 GeV. Studies using multi-variate analysis techniques for lepton reconstruction are also presented. With including this method, the expected lower limits on m(\tilde{Chi}^0_2) are found to improve by about 15 GeV in the regions with \Delta m larger than 10 GeV, for both parameters sets in the Wino/Bino scenarios.