  Current measurements of the large-scale structure of galaxies are able to
place an $\sim 0.5 ~ \rm eV$ upper limit on the absolute mass scale of
neutrinos. An order-of-magnitude improvement in raw sensitivity, together with
an insensitivity to systematic effects, is needed to reach the lowest value
allowed by particle physics experiments. We consider the prospects of
determining both the neutrino mass scale and the number of of massive neutrinos
using future redshift surveys, specifically those undertaken with the Square
Kilometre Array (SKA), with and without additional constraints from the
upcoming Planck CMB experiment. If the sum of the neutrino masses $\sum m_i
\gtsimeq 0.25 ~ \rm eV$ then the imprint of neutrinos on large-scale structure
(LSS) should be enough, on its own, to establish the neutrino mass scale and,
considered alongside CMB constraints, it will also determine the number of
massive neutrinos $N_{\nu}$, and hence the mass hierarchy. If $\sum m_i \sim
0.05 ~ \rm eV$, at the bottom end of the allowed range, then a combination of
LSS, CMB and particle physics constraints should be able to determine $\sum
m_i$, $N_{\nu}$ and the hierarchy. If $\sum m_i$ is in the specific range
$0.1-0.25 ~ \rm eV$, then a combination of LSS, CMB and particle physics
experiments should determine $\sum m_i$, but not $N_{\nu}$ or the hierarchy.
Once an SKA-like LSS survey is available there are good prospects of obtaining
a full understanding of the conventional neutrino sector, and a chance of
finding evidence for sterile neutrinos.
