  In this article we study minimal homeomorphisms(all orbits are dense) of the
tori $T^{n},$ $n<5.$ The linear part of a homeomorphism $\phi $ of $T^{n}$ is
the linear mapping $L$ induced by $\phi $ on the first homology group of
$T^{n}$. It follows from the Lefschetz fixed point theorem that 1 is an
eigenvalue of $L$ if $\phi $ minimal. We show that if $\phi $ is minimal and
$n<5$ then $L$ is quasi-unipontent, i.e., all the eigenvalues of $L$ are roots
of unity and conversely if $L\in GL(n,\Z)$ is quasi-unipotent and 1 is an
eigenvalue of $L$ then there exists a $ C^{\infty}$ minimal skew-product
diffeomorphism $\phi $ of $T^{n}$ whose linear part is precisely $L.$ We do not
know if these results are true for $n>4$. We give a sufficient condition for a
smooth skew-product diffeomorphism of a torus of arbitrary dimension to be
smoothly conjugate to an affine transformation.
