  The upcoming Mu3e experiment searches for the lepton flavour violating decay
$\mu^+\,\rightarrow\,e^+ e^- e^+$ with the aim of a final sensitivity of one
signal decay in $10^{16}$ observed muon decays, an improvement over the
preceding SINDRUM experiment by four orders of magnitude. In the first phase,
the experiment will be operated at an existing intense muon beam line at the
Paul Scherrer Institute. With muon stopping rates of about
$10^{8}\text{s}^{-1}$, a single-event sensitivity of $2\cdot 10^{-15}$ can be
achieved. For the ultimate sensitivity, a new high intensity muon beam line is
required. In order to suppress background, the tracking detector is designed to
measure low momentum electron and positron tracks with excellent precision by
making use of very thin silicon pixel sensors. In addition, scintillating
fibres and tiles provide precise timing information. Currently, the
collaboration is finalizing the detector design and preparing for construction
and commissioning.
