  In this thesis, we study the Nicolai maps of the 2-dimensional Wess-Zumino
model, $\mathcal{N}=1$ super Yang-Mills and $\mathcal{N}=4$ super Yang-Mills.
We compute the Nicolai map of the 2-dimensional Wess-Zumino model up to the
fifth order in the coupling. In $\mathcal{N}=1$ super Yang-Mills, we introduce
the notion of on- and off-shell Nicolai maps. The on-shell Nicolai map of
$\mathcal{N}=1$ super Yang-Mills exists in d=3, 4, 6 and 10 dimensions but is
constrained to the Landau gauge. We compute this map up to the fourth order.
The off-shell Nicolai map exists only in d=4 dimensions but for general gauges.
We compute it in the axial gauge up to the second order. We show that the
$\mathcal{N}=4$ super Yang-Mills Nicolai map can be obtained from the Nicolai
map of 10-dimensional $\mathcal{N}=1$ super Yang-Mills by dimensional
reduction.
  Inverse Nicolai maps allow for a fermion (and ghost) free quantization of
supersymmetric (gauge) theories. We apply this property to compute the vacuum
expectation value of the infinite straight line Maldacena-Wilson loop in
$\mathcal{N}=4$ super Yang-Mills to the sixth order.
  In the second part of this thesis, we derive the explicit field content of
the 1/2-BPS stress tensor multiplet in $\mathcal{N}=4$ super Yang-Mills, which
contains the R-symmetry current and the energy-momentum tensor.
  The original version of this thesis, as submitted in May 2023 to the Humboldt
University of Berlin, is available under the DOI
https://doi.org/10.18452/26406.

High Energy Physics - Theory