  The 4-dimensional metric $f(\R)$ theories of gravity are cast into
connection-dynamical formalism with real $\SU(2)$-connections as configuration
variables. Through this formalism, the classical metric $f(\R)$ theories are
quantized by extending the loop quantization scheme of general relativity. Our
results imply that the non-perturbative quantization procedure of loop quantum
gravity is valid not only for general relativity but also for a rather general
class of 4-dimensional metric theories of gravity.
