  We study the mixing of the Gluino-Glue operator in ${\cal N}$=1
Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and
on the lattice. We calculate its renormalization, which is not only
multiplicative, due to the fact that this operator can mix with non-gauge
invariant operators of equal or, on the lattice, lower dimension. These
operators carry the same quantum numbers under Lorentz transformations and
global gauge transformations, and they have the same ghost number.
  We compute the one-loop quantum correction for the relevant two-point and
three-point Green's functions of the Gluino-Glue operator. This allows us to
determine renormalization factors of the operator in the
$\overline{\textrm{MS}}$ scheme, as well as the mixing coefficients for the
other operators. To this end our computations are performed using dimensional
and lattice regularizations. We employ a standard discretization where gluinos
are defined on lattice sites and gluons reside on the links of the lattice; the
discretization is based on Wilson's formulation of non-supersymmetric gauge
theories with clover improvement. The number of colors, $N_c$, the gauge
parameter, $\beta$, and the clover coefficient, $c_{\rm SW}$, are left as free
parameters.
