  We give exposition of a Liouville theorem established in \cite{Li3} which is
a novel extension of the classical Liouville theorem for harmonic functions. To
illustrate some ideas of the proof of the Liouville theorem, we present a new
proof of the classical Liouville theorem for harmonic functions. Applications
of the Liouville theorem, as well as that of earlier ones in \cite{Li2}, can be
found in \cite{Li3, Li4} and \cite{W}.
