  Fractional quantum Hall (FQH) liquids contain extremely rich internal
structures which represent a whole new kind of ordering. We discuss
characterization and classification of the new orders (which is called
topological orders). We also discuss the edge excitations in FQH liquids, which
form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at
the edges also have very rich structures as a reflection of the rich
topological orders in the bulk. Thus, edge excitations provide us a practical
way to measure topological orders in experiments.
