  We define the Schwarzian Field Theory as a finite measure on
$\mathrm{Diff}^1(\mathbb{T})/\mathrm{PSL}(2,\mathbb{R})$ and compute its
generalised partition functions exactly using methods of stochastic analysis.
The Schwarzian Field Theory has attracted recent attention due to its role in
the analysis of the Sachdev--Ye--Kitaev model and as the proposed holographic
dual to Jackiw--Teitelboim gravity. In two companion papers by Losev, the
predicted exact cross-ratio correlation functions for non-crossing Wilson lines
and the large deviations are derived from the probability measure.}
