  The IA-automorphism group $\operatorname{IA}_n$ of the free group $F_n$ of
rank $n$ is a normal subgroup of the automorphism group
$\operatorname{Aut}(F_n)$ of $F_n$. We study the Albanese homology of
$\operatorname{IA}_n$, which is the quotient of the rational homology of
$\operatorname{IA}_n$ defined as the image of the map induced by the
abelianization map of $\operatorname{IA}_n$ on homology. The Albanese homology
of $\operatorname{IA}_n$ is an algebraic
$\operatorname{GL}(n,\mathbb{Q})$-representation. We determine the
representation structure of the Albanese homology of $\operatorname{IA}_n$ for
$n$ greater than or equal to three times the homological degree. We also
determine the structure of the stable Albanese homology of the analogue of
$\operatorname{IA}_n$ to the outer automorphism group of $F_n$. Moreover, we
identify the relation between the stable Albanese (co)homology of
$\operatorname{IA}_n$ and the stable cohomology of $\operatorname{Aut}(F_n)$
with certain twisted coefficients.
