  In primary school, we were told that there are four phases of matter: solid,
liquid, gas, and plasma. In college, we learned that there are much more than
four phases of matter, such as hundreds of crystal phases, liquid crystal
phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter
are so rich, it is amazing that they can be understood systematically by the
symmetry breaking theory of Landau. However, there are even more interesting
phases of matter that are beyond Landau symmetry breaking theory. In this
paper, we review new "topological" phenomena, such as topological degeneracy,
that reveal the existence of those new zero-temperature phases -- topologically
ordered phases. Microscopically, topologically orders are originated from the
patterns of long-range entanglement in the ground states. As a truly new type
of order and a truly new kind of phenomena, topological order and long-range
entanglement require a new language and a new mathematical framework, such as
unitary fusion category and modular tensor category to describe them. In this
paper, we will describe a simple mathematical framework based on measurable
quantities of topological orders $(S,T,c)$ proposed around 1989. The framework
allows us to systematically describe/classify 2+1D topological orders (ie
topological orders in local bosonic/spin/qubit systems)..
