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This thesis concerns the search for relativistic magnetic monopoles using data taken in 2008/2009 with the partially completed IceCube detector. The outline of this work is as follows: Chapter 2 provides the theoretical background of magnetic monopoles and their interaction with with matter. Chapter 3 introduces the IceCube detector, followed by a description of the signatures of both signal and background events in Chapter 4. In Chapter 5 an overview of the simulated data used for the analysis and its generation is given. Chapters 6 and 7 then summarize the variables and cut conditions applied in the analysis. Systematic uncertainties are discussed in Chapter 8. The final results are presented in Chapter 9 followed by some concluding remarks in Chapter 10.