We present the first characterization of the diffuse gas and metals in the circumgalactic medium of 96 z = 2.9-3.8 Ly$alpha$ emitters (LAEs) detected with the Multi-Unit Spectroscopic Explorer (MUSE) in fields centered on 8 bright background quasars as part of our MUSEQuBES survey. The LAEs have relatively low Ly$alpha$ luminosities (~$10^{42}$ erg/s) and star formation rates ~1 $M_odot$/yr, which for main sequence galaxies corresponds to stellar masses of only ~$10^{8.6}$ $M_{odot}$. The median transverse distance between the LAEs and the quasar sightlines is 165 proper kpc (pkpc). We stacked the high-resolution quasar spectra and measured significant excess HI and CIV absorption near the LAEs out to 500 km/s and at least 250 pkpc (corresponding to ~7 virial radii). At < 30 km/s from the galaxies the median HI and CIV optical depths are enhanced by an order of magnitude. The average rest-frame equivalent width of Ly$alpha$ absorption is comparable to that for Lyman-break galaxies (LBGs) at z~2.3 and ~L* galaxies at z~0.2, but considerably higher than for sub-L*/dwarf galaxies at low redshift. The CIV equivalent width is comparable to those measured for low-z dwarf galaxies and z~2.3 LBGs but significantly lower than for z~2.3 quasar-host galaxies. The absorption is significantly stronger around the ~ 1/3 of our LAEs that are part of groups, which we attribute to the large-scale structures in which they are embedded. We do not detect any strong dependence of either the HI or CIV absorption on transverse distance (over the range 50-250 pkpc), redshift, or the properties of the Ly$alpha$ emission line (luminosity, full width at half maximum, or equivalent width). However, for HI, but not CIV, the absorption at < 100 km/s from the LAE does increase with the star formation rate. This suggests that LAEs surrounded by more neutral gas tend to have higher star formation rates.
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