The Mu3e experiment is a novel experiment to search for the lepton flavour violating (LFV) decay μ+ → e+e−e+, with an ultimate sensitivity to a branching ratio of one in 2×10^15 in phase I and one in 10^16 muon decays for phase II. This is an improvement in sensitivity by four orders of magnitude compared to previous searches by the SINDRUM experiment. Since this decay is suppressed to unobservable levels in the Standard Model of particle physics, any measurement of this decay would be a clear sign of new physics. The experiment is currently under construction and will take place at the Paul Scherrer Institute in Switzerland. In order to achieve this number of muon decays, the Paul Scherrer Institute (PSI) is utilizing the worlds most intense proton beam, which is used to produce very intense 10^8 μ/s at πE5 beamline (phase I) and a new high-intensity muon beam line HiMB is providing 10^9 μ/s (phase II). To achieve the proposed sensitivity, the Mu3e experiment requires excellent vertex, timing and momentum resolutions. These are needed to reduce the main background processes, such as Internal conversion and accidental coincidences caused by two or more Michel decays. This paper will present an overview of the Mu3e experiment with the performance of the phase I Mu3e detector, and how this sensitivity is achieved by high voltage monolithic active pixel sensors for high spatial resolution and scintillating fibres and tiles providing precise timing information at high particle rates.