  We construct an action, which governs the dynamics of the
Ba\~nados-Teitelboim-Zanelli (BTZ) black hole and perform the canonical
quantization. The quantum action is given by a $SL(2,R)$ Wess-Zumino-Witten
model on the boundary coupled to the classical anti-de Sitter background,
representing a massless BTZ black hole. The coupling, determined by a
one-cocyle condition, is found to give dominant contribution to the central
charge of Virasoro algebra. The entropy of the BTZ black hole is discussed from
the point view of the AdS/CFT correspondence and an explanation is given to the
puzzle of black hole entropy in the BTZ case. The BTZ black hole is a quantum
object and the BTZ black hole with finite mass should be considered as a
quantum excitation of the massless one.
