Supersymmetry (SUSY) is one of the most promising theories for physics beyond the standard model as it explains many of the current problems with the standard model of particle physics (SM). For instance, in many minimal supersymmetric extensions of the SM the lightest supersymmetric particle (LSP) is a stable weakly interacting particle and is therefore an excellent dark matter candidate. However, searches at Tevatron, LEP and the LHC have not been able to find any signs of SUSY so far. This lack of indications for SUSY may be explained if the LSP and the next-to-lightest SUSY particle have a small mass difference, a scenario which is referred to as compressed SUSY. In particular, SUSY scenarios with a light top squark (t) are well motivated since they allow for a natural mechanism to stabilize the loop corrections to the Higgs mass by partially cancelling the contributions coming from the top quark. Additionally, the co-annihilation cross section between the LSP and a light top squark can predict the dark matter relic density which is observed in the universe. This thesis presents a search for the pair production of the top squarks in SUSY models with compressed mass spectra using the 2016 proton-proton collision data collected at the CMS detector of the LHC. The single lepton channel of the four-body (t -> b f f' LSP) and chargino-mediated (t -> b X1+ -> b f f' LSP) decays of the top squark are investigated. The data are found to be compatible with the predicted SM background processes and the results are used to set limits on the production cross section of the top squark. Assuming 100% branching fraction of each decay mode, top squark masses of up to 500 and 540GeV are excluded at 95% confidence level for the four-body and chargino-mediated decays respectively.