  We consider topological insulators and superconductors with discrete
symmetries and clarify the relevant index theory behind the periodic table
proposed by Kitaev.
  An effective Hamiltonian determines the analytical index, which can be
computed by a topological index. We focus on the spatial dimensions one, two
and three, and only consider the bulk theory.
  In two dimensions, the $\mathbb{Z}$-valued invariants are given by the first
Chern number. Meanwhile, $\mathbb{Z}_2$-valued invariants can be computed by
the odd topological index and its variations.
  The Bott-Kitaev periodic table is well-known in the physics literature, we
organize the topological invariants in the framework of KR-theory.
