We report X-ray, optical, and near-infrared monitoring of the new X-ray transient MAXI J1820$+$070 discovered with MAXI on 2018 March 11. Its X-ray intensity reached $sim 2$ Crab in 2--20 keV at the end of March, and then gradually decreased until the middle of June. In this period, the X-ray spectrum was described by Comptonization of the disk emission, with a photon index of $sim$1.5 and an electron temperature of $sim$50 keV, which is consistent with a black hole X-ray binary in the low/hard state. The electron temperature and the photon index were slightly decreased and increased with increasing flux, respectively. The source showed significant X-ray flux variation on timescales of seconds. This short-term variation was found to be associated with changes in the spectral shape, and the photon index became slightly harder at higher fluxes. This suggests that the variation was produced by a change in the properties of the hot electron cloud responsible for the strong Comptonization. Modeling a multi-wavelength SED around the X-ray flux peak at the end of March, covering the near-infrared to X-ray bands, we found that the optical and near-infrared fluxes were likely contributed substantially by the jet emission. Before this outburst, the source was never detected in the X-ray band with MAXI (with a 3$sigma$ upper limit of $sim$0.2 mCrab in 4--10 keV, obtained from the 7-year data in 2009--2016), whereas weak optical and infrared activity was found at their flux levels $sim$3 orders of magnitude lower than the peak fluxes in the outburst.
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