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Topological order, as a new kind of organization in many-body systems,
cannot be characterized by local order parameters and long range
correlations of local operators. We need to use a new set of quantum numbers
to characterize topological order, such as ground state degeneracy,
non-Abelian phases from modulo transformation, edge states, and pattern of long range
entanglements. Due to the presence of long range entanglements,
many traditional ways of constructing many-body states fail
to produce topological ordered states. I will review several
new ways to construct many-body states that may contain topological order.
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