Abstract
This article is an introduction to the nontrivial topological properties associated with the special band structure in the electron systems with strong spin-orbital coupling, where a new topological phase known as topological insulator emerges. A Z2 topological invariant can distinguish a topological insulator from a trivial band insulator in time-reversal invariant systems. The theoretically predicted quantum spin Hall effect and three dimensional topological insulators have been discovered experimentally. We provide an introduction to the understandings of topological insulating state, interaction effect and fractional quantum spin Hall effect, as well as their numerical identification.
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