The COMET Experiment at J-PARC aims to search for the lepton-flavour violating process of muon to electron conversion in a muonic atom, $\mu^{-}N \rightarrow \mathrm{e}^{-}N$, with a 90\% confidence level branching-ratio limit of $6 \times 10^{-17}$, in order to explore the parameter region predicted by most well-motivated theoretical models beyond the Standard Model. In order to realize the experiment effectively, a staged approach to deployment is employed; COMET Phase-I \& II. At the Phase-I experiment, a precise muon-beam measurement will be conducted, and a search for $\mu^{-}N \rightarrow \mathrm{e}^{-}N$ will also be carried out with an intermediate sensitivity of $7 \times 10^{-15}$ (90\% CL upper limit).\\

The dedicated proton beam-line was recently completed and its commissioning run (COMET Phase-$\alpha$) was successfully conducted in 2023. In this paper, the construction status and some prospects of the experiment are presented in addition to the experimental overview.