The aim of this talk is to explore the possibility of a mod $p$ analog
for the theories of complex
representations of $p$-adic reductive groups and of Hecke algebras
presented in Shaun Stevens' course.
I will focus on the case of ${\rm GL}_n$.
I will give results about the related structures of the (pro-$p$)
Iwahori-Hecke algebra and the spherical Hecke algebra with integer/mod
$p$ c\oe fficients and will discuss the properties of the natural link
between pro-$p$ Hecke modules and smooth mod $p$ representations of
$p$-adic ${\rm GL}_n$.