The Mu3e experiment aims to find or exclude the lepton flavour violating decay μ→ e e e at branching fractions above 1 0− 16. A first phase of the experiment using an existing beamline at the Paul Scherrer Institute (PSI) is designed to reach a single event sensitivity of 2⋅ 1 0− 15. We present an overview of all aspects of the technical design and expected performance of the phase I Mu3e detector. The high rate of up to 1 0 8 muon decays per second and the low momenta of the decay electrons and positrons pose a unique set of challenges, which we tackle using an ultra thin tracking detector based on high-voltage monolithic active pixel sensors combined with scintillating fibres and tiles for precise timing measurements.