  The ALMA-ALPINE [CII] survey is aimed at characterizing the properties of a
sample of normal star-forming galaxies (SFGs). The ALMA Large Program to
INvestigate (ALPINE) features 118 galaxies observed in the [CII]-158$\mu$m line
and far infrared (FIR) continuum emission during the period of rapid mass
assembly, right after the end of the HI reionization, at redshifts of 4<z<6. We
present the survey science goals, the observational strategy, and the sample
selection of the 118 galaxies observed with ALMA, with an average beam minor
axis of about 0.85 arcsec, or $\sim$5 kpc at the median redshift of the survey.
The properties of the sample are described, including spectroscopic redshifts
derived from the UV-rest frame, stellar masses, and star-formation rates
obtained from a spectral energy distribution (SED) fitting. The observed
properties derived from the ALMA data are presented and discussed in terms of
the overall detection rate in [CII] and FIR continuum, with the observed
signal-to-noise distribution. The sample is representative of the SFG
population in the main sequence at these redshifts. The overall detection rate
in [CII] is 64% for a signal-to-noise ratio (S/N) threshold larger than 3.5
corresponding to a 95% purity (40% detection rate for S/N>5). Based on a visual
inspection of the [CII] data cubes together with the large wealth of ancillary
data, we find a surprisingly wide range of galaxy types, including 40% that are
mergers, 20% extended and dispersion-dominated, 13% compact, and 11% rotating
discs, with the remaining 16% too faint to be classified. This diversity
indicates that a wide array of physical processes must be at work at this
epoch, first and foremost, those of galaxy mergers. This paper sets a reference
sample for the gas distribution in normal SFGs at 4<z<6.
