Charged-particle tracking in the international Muon Ionisation Cooling Experiment (MICE) will be performed using two solenoidal spectrometers, each instrumented with a tracking detector based on 350 {mu}m diameter scintillating fibres. The design and construction of the trackers is described along with the quality-assurance procedures, photon-detection system, readout electronics, reconstruction and simulation software and the data-acquisition system. Finally, the performance of the MICE tracker, determined using cosmic rays, is presented.
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