  We give a motivation and gentle introduction into the regularity structure
and model introduced by Otto, Sauer, Smith and Weber, which fall into the
framework of Hairer, but have a greedier index set than the one given by trees.
We do this here for a simple quasi-linear parabolic equation and assume that
the driving noise is so regular that no renormalization is needed. We introduce
the abstract model space $\mathsf{T}$ and its grading, the pre-model
$\mathbf{\Pi}$, the centered model $\Pi_x$, the structure group $\mathsf{G}$,
and the re-centering transformations $\Gamma_{xy}$. Using integration and
reconstruction, we establish the desired estimates on $\Pi_x$ and
$\Gamma_{xy}$, which here are deterministic since we deal with the regular
case.
