Mu3e will search for charged Lepton Flavor Violation in the neutrinoless muon decay $\mu^+ \rightarrow e^+ e^- e^+$ with a sensitivity down to $10^{-16}$ (90\% C.L.) using the world most intense continuous muon beam at PSI. This search requires a large acceptance detector capable of coping with rates of up to $2 \times 10^9$ stopped muons per second with excellent momentum, spatial, and time resolution. The Mu3e detector is based on thin monolithic active silicon pixel sensors for tracking in conjunction with scintillating fibers and tiles for timing measurements. The Mu3e apparatus is under constructions and first data is expected in 2020.