Fundamental work of P. Deligne on differential equations is the following. Let $X/\mathbb{C}$ be a smooth, connected algebraic variety. The Riemann--Hilbert correspondence associates to an integrable connection with regular singularities a representation of the topological fundamental group $\pi_1^{top}$. This is an equivalence of Tannaka categories and it provides an algebraic interpretation of the algebraic hull $\pi_1^{top,alg}$ of $\pi_1^{top}$.

For a variety $X$ in characteristic $p>0$ the good differential equations, called stratified bundles, are rather complicated objects. The Tannaka group of the category of stratified bundles on $X$ is seen as a replacement for a non existing topological fundamental group.

There are relations with the etale fundamental group (which exists in characteristic $p>0$) and there is a theory of regular singularities which does not involve resolution of singularities. The theory of stratifications works quite well. The main difficulty in characteristic $p>0$ is the lack of explicit examples. In this lecture we provide examples and methods for their construction in the 1-dimensional case.