  We study Cameron-Liebler $k$-sets in the affine geometry, so sets of
$k$-spaces in $\text{AG}(n, q)$. This generalizes research on Cameron-Liebler
$k$-sets in the projective geometry $\text{PG}(n, q)$. Note that in algebraic
combinatorics, Cameron-Liebler $k$-sets of $\text{AG}(n, q)$ correspond to
certain equitable bipartitions of the Association scheme of $k$-spaces in
$\text{AG}(n, q)$, while in the analysis of Boolean functions, they correspond
to Boolean degree $1$ functions of $\text{AG}(n, q)$. We define Cameron-Liebler
$k$-sets in $\text{AG}(n, q)$ by intersection properties with $k$-spreads and
show the equivalence of several definitions. In particular, we investigate the
relationship between Cameron-Liebler $k$-sets in $\text{AG}(n, q)$ and
$\text{PG}(n, q)$. As a by-product, we calculate the character table of the
association scheme of affine lines. Furthermore, we characterize the smallest
examples of Cameron-Liebler $k$-sets. This paper focuses on $\text{AG}(n, q)$
for $n > 3$, while the case for Cameron-Liebler line classes in $\text{AG}(3,
q)$ was already treated separately.
