  In the first part of this thesis a coupled truncated set of Dyson-Schwinger
equations (DSEs) including the one for the gluon-propagator is solved
self-consistently over the whole momentum range. In Landau gauge the truncation
of the coupled set of DSEs for the ghost and gluon propagators is improved by
the first full inclusion of the sunset diagram. A solution method which avoids
all overlapping divergences is presented. In the Maximal Abelian gauge a
truncation is developed with respectively one infrared and one ultraviolet
leading diagram included. A first solution of the ghost equation is presented.
In the second part generalizations of the Kugo-Ojima confinement scenario to
other gauges than the linear covariant gauge are investigated. In the
generalized covariant gauge no contradiction is found by using a Faddeev-Popov
conjugation invariant assignment of the asymptotic fields. In the last section
a gauge-independent generalized criterion is developed which allows for the
identification of the Coulomb, Higgs- and confining phases of Yang-Mills theory
in terms of the infrared limit of the Dyson-Schwinger equation of the gauge
boson propagator. While in a Coulomb phase the photon is massless, dominating
the infrared of the equation, in the Higgs phase this equation is dominated by
the physical mass of the gauge boson. In the confining phase the equation is
saturated by unphysical degrees of freedom in the infrared limit only. This
proposal is tested in a variety of gauges and the corresponding unphysical
terms are identified.
