Molecular gas in distant galaxies from ALMA studies
  ALMA is now fully operational, and has been observing in early science mode
since 2011.
  The millimetric (mm) and sub-mm domain is ideal to tackle galaxies at high
redshift, since the emission peak of the dust at 100$\mu$m is shifted in the
ALMA bands (0.3mm to 1mm) for z=2 to 9, and the CO lines, stronger at the
high-J levels of the ladder, are found all over the 0.3-3mm range.
  Pointed surveys and blind deep fields have been observed, and the wealth of
data collected reveal a drop at high redshifts (z $>$ 6) of dusty massive
objects, although surprisingly active and gas-rich objects have been unveiled
through gravitational lensing. The window of the reionization epoch is now wide
open, and ALMA has detected galaxies at z=8-9 mainly in continuum, [CII] and
[OIII] lines. Galaxies have a gas fraction increasing steeply with redshift, as
(1+z)$^2$, while their star formation efficiency increases also but more
slightly, as (1+z)$^{0.6}$ to (1+z)$^1$. Individual object studies have
revealed luminous quasars, with black hole masses much higher than expected,
clumpy galaxies with resolved star formation rate compatible with the
Kennicutt-Schmidt relation, extended cold and dense gas in a circumgalactic
medium, corresponding to Lyman-$\alpha$ blobs, and proto-clusters, traced by
their brightest central galaxies.
