  The Mu3e experiment aims to find or exclude the lepton flavour violating
decay $\mu^+\to e^+e^-e^+$ with a sensitivity of one in 10$^{16}$ muon decays.
The first phase of the experiment is currently under construction at the Paul
Scherrer Institute (PSI, Switzerland), where beams with up to 10$^8$ muons per
second are available. The detector will consist of an ultra-thin pixel tracker
made from High-Voltage Monolithic Active Pixel Sensors (HV-MAPS), complemented
by scintillating tiles and fibres for precise timing measurements. The
experiment produces about 100 Gbit/s of zero-suppressed data which are
transported to a filter farm using a network of FPGAs and fast optical links.
On the filter farm, tracks and three-particle vertices are reconstructed using
highly parallel algorithms running on graphics processing units, leading to a
reduction of the data to 100 Mbyte/s for mass storage and offline analysis. The
paper introduces the system design and hardware implementation of the Mu3e data
acquisition and filter farm.
