  The cosmological case for a next generation radio observatory, the Square
Kilometer Array, is discussed and reviewed. An instrument like the SKA would be
able to measure galaxy redshifts of normal late-type galaxies, via the 21 cm
line of HI, out to redshifts of $\sim 3$. Not only would such very deep
redshift surveys enable us to map the large scale galaxy distribution and probe
the large scale structure of the universe out to previously unexplored scales,
it would also allow for the first time to obtain direct observational data on
the evolution of this structure. Other promising applications concern the
mapping of the local velocity field of the universe, study of the formation and
evolution of galaxies, and determining the global cosmological parameters
$H_0$, $q_0$ and $\Lambda$ through the application of classical cosmological
tests like source counts. Particularly emphasized is the redshift survey
capability of the SKA. A review is given of the current knowledge of the galaxy
distribution, starting from an inventarisation of nearby cosmic structures,
through a discussion of how it all fits together in a coherent ``foamlike
pattern''. After providing a short overview of the basics of theories of
structure formation, a description is provided of different observational
strategies to probe the structure of the universe out to larger depths, ranging
from pencil-beam surveys and cluster surveys out to the new and ambitious
complete and deep galaxy redshift surveys like the 2dF and the Sloan survey. It
is argued that a survey with the SKA would be a natural and complementary
follow-up. We finally conclude with a specification of the technical
requirements for the SKA to make it into an instrument ideally suited for these
purposes.
