  Given a Quantum Field Theory, with a particular content of fields and a
symmetry associated with them, if one wants to study the evolution of the
couplings via a Wilsonian renormalisation group, there is still a freedom on
the construction of a flow equation, allowed by scheme independence. In the
present thesis, making use of this choice, we first build up a generalisation
of the Polchinski flow equation for the massless scalar field, and, applying it
to the calculation of the beta function at one loop for the characteristic
self-interaction, we test its universality beyond the already known cutoff
independence. Doing so we also develop a method to perform the calculation with
this generalised flow equation for more complex cases. In the second part of
the thesis, the method is extended to SU(N) Yang-Mills gauge theory, regulated
by incorporating it in a spontaneously broken SU(N|N) supergauge group. Making
use of the freedom allowed by scheme independence, we develop a flow equation
for a SU(N|N) gauge theory, which preserves the invariance step by step
throughout the flow and demonstrate the technique with a compact calculation of
the one-loop beta function for the SU(N) Yang-Mills physical sector of SU(N|N),
achieving a manifestly universal result, and without gauge fixing, for the
first time at finite N.
