  This paper aims to construct foliations $\mathcal{F}$ that are stable,
meaning that any other foliation close to $\mathcal{F}$ is conjugate to
$\mathcal{F}$ by a diffeomorphism. Our main result yields examples of stable
Riemannian foliations $\mathcal{F}$ with dense leaves. To our knowledge, these
are the first examples of stable Riemannian foliations that are not Hausdorff.
