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This dissertation describes a search for the associated production of the supersymmetric particles, the chargino and the neutralino, through their R-parity conserving decays to three leptons and missing energy. This search is carried out using the data collected at the CDF experiment at the Tevatron {radical}s = 1.96 TeV p{bar p} collider at Fermilab. The results are obtained by combining five independent channels with varying signal to background ratio. Overall, a total of 6.4 {+-} 1.1 background events from standard model processes and 11.4 {+-} 1.1 signal events for a particular choice of mSUGRA model parameters are expected. The observation of 7 events in data is consistent with the standard model background expectation, and the mSUGRA model is constrained. Limits are set on the cross section of Chargino-Neutralino pair production, and a limit on the mass of the chargino is extracted. A method of obtaining model-independent results is also discussed

Search for super symmetry at the Tevatron using the trilepton signature