  The low $x$ limit of deep inelastic electron proton scattering is considered
using methods of perturbative QCD. In the first part we investigate the
phenomenological consequences of the resummation of leading logarithms in $1/x$
given by the BFKL pomeron. We apply the BFKL pomeron to the inclusive structure
function $F_2$, to the diffractive production of vector mesons at large
momentum transfer, to inclusive photon diffractive dissociation in DIS and to
quark-antiquark production with large transverse momenta in DIS diffractive
dissociation. For the last process we perform extensive numerical calculations
based on the double logarithmic approximation. The BFKL pomeron is known to
violate unitarity. In the second part the first next-to-leading corrections
which have to be taken into account to restore unitarity of the scattering
amplitude are investigated. A compact configuration space representation of the
two to four gluon transition vertex is derived. Conformal symmetry of the
vertex is proven and its relation to a conformal covariant three point function
is established. The important role of the spectral function $\chi_4$ of the
four gluon state is pointed out. We relate this function to the twist expansion
of the four gluon amplitude. Motivated by this relation we develop a method to
perform the twist expansion of the amplitude. Based upon first results of our
analysis we draw conclusions concerning the singularity structure of the
function $\chi_4$.
