  In the last 20 years, loop quantum gravity, a background independent approach
to unify general relativity and quantum mechanics, has been widely
investigated. The aim of loop quantum gravity is to construct a mathematically
rigorous, background independent, nonperturbative quantum theory for the
Lorentzian gravitational field on a four-dimensional manifold. In this
approach, the principles of quantum mechanics are combined with those of
general relativity naturally. Such a combination provides us a picture of
"quantum Riemannian geometry", which is discrete at a fundamental scale. In the
investigation of quantum dynamics, the classical expressions of constraints are
quantized as operators. The quantum evolution is contained in the solutions of
the quantum constraint equations. On the other hand, the semi-classical
analysis has to be carried out in order to test the semiclassical limit of the
quantum dynamics.
  In this thesis, the structure of the dynamical theory in loop quantum gravity
is presented pedagogically. The outline is as follows: first we review the
classical formalism of general relativity as a dynamical theory of connections.
Then the kinematical Ashtekar-Isham-Lewandowski representation is introduced as
a foundation of loop quantum gravity. We discuss the construction of a
Hamiltonian constraint operator and the master constraint programme, for both
the cases of pure gravity and matter field coupling. Finally, some strategies
are discussed concerning testing the semiclassical limit of the quantum
dynamics.
