This paper discusses the topological insulators with inversion symmetry, focusing on the $Z_2$ topological invariants that characterize their bulk and surface properties. The authors show that the presence of inversion symmetry simplifies the evaluation of these invariants, which can be determined from the parity of the occupied Bloch wavefunctions at time-reversal invariant points in the Brillouin zone. They predict several specific materials, such as semiconducting alloys Bi$_{1-x}$Sb$_x$, α-Sn, and HgTe under uniaxial strain, to be strong topological insulators. The paper also provides an expanded discussion of the formulation of $Z_2$ invariants in two and three dimensions, and their implications for experiments. The authors emphasize the robustness of the strong topological insulator phase, characterized by a single $Z_2$ invariant, against weak disorder and interactions, while the weak topological invariants are more fragile and depend on translational symmetry.This paper discusses the topological insulators with inversion symmetry, focusing on the $Z_2$ topological invariants that characterize their bulk and surface properties. The authors show that the presence of inversion symmetry simplifies the evaluation of these invariants, which can be determined from the parity of the occupied Bloch wavefunctions at time-reversal invariant points in the Brillouin zone. They predict several specific materials, such as semiconducting alloys Bi$_{1-x}$Sb$_x$, α-Sn, and HgTe under uniaxial strain, to be strong topological insulators. The paper also provides an expanded discussion of the formulation of $Z_2$ invariants in two and three dimensions, and their implications for experiments. The authors emphasize the robustness of the strong topological insulator phase, characterized by a single $Z_2$ invariant, against weak disorder and interactions, while the weak topological invariants are more fragile and depend on translational symmetry.