  Topological band insulators (TBIs) are bulk insulating materials which
feature topologically protected metallic states on their boundary. The existing
classification departs from time-reversal symmetry, but the role of the crystal
lattice symmetries in the physics of these topological states remained elusive.
Here we provide the classification of TBIs protected not only by time-reversal,
but also by crystalline symmetries. We find three broad classes of topological
states: (a) Gamma-states robust against general time-reversal invariant
perturbations; (b) Translationally-active states protected from elastic
scattering, but susceptible to topological crystalline disorder; (c) Valley
topological insulators sensitive to the effects of non-topological and
crystalline disorder. These three classes give rise to 18 different
two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route
for the systematic search for new types of TBIs.
