  In the first chapter we give an introduction to hard diffractive scattering
in QCD to introduce basic concepts and terminology. In the second chapter we
make predictions for the evolution of skewed parton distributions in a proton
in the LLA. We calculate the DGLAP-type evolution kernels in the LLA and solve
the skewed GLAP evolution equations with a modified version of the
CTEQ-package. In the third chapter, we discuss the algorithms used in the LO
evolution program for skewed parton distributions in the DGLAP region, discuss
the stability of the code and reproduce the LO diagonal evolution within less
than 0.5% of the original CTEQ-code. In chapter 4, we show that factorization
holds for the deeply virtual Compton scattering amplitude in QCD, up to power
suppressed terms, to all orders in perturbation theory. In chapter 5, we
demonstrate that perturbative QCD allows one to calculate the absolute cross
section of diffractive, exclusive production of photons (DVCS) at large $Q^2$
at HERA, while the aligned jet model allows one to estimate the cross section
for intermediate $Q^2 \sim 2 GeV^2$. We find a significant DVCS counting rate
for the current generation of experiments at HERA and a large azimuthal angle
asymmetry for HERA kinematics. In the last chapter, we propose a new
methodology of gaining shape fits to skewed parton distributions and, for the
first time, to determine the ratio of the real to imaginary part of the DIS
amplitude. We do this by using several recent fits to $F_2(x,Q^2)$ to compute
the asymmetry $A$ for the combined DVCS and Bethe-Heitler cross section. In the
appendix, we give an application of distributional methods as discussed
abstractly in chapter 4.
