  We introduce the basic elements of the theory of parametrized
$\infty$-categories and functors between them. These notions are defined as
suitable fibrations of $\infty$-categories and functors between them. We give
as many examples as we are able at this stage. Simple operations, such as the
formation of opposites and the formation of functor $\infty$-categories, become
slightly more involved in the parametrized setting, but we explain precisely
how to perform these constructions. All of these constructions can be performed
explicitly, without resorting to such acts of desperation as straightening. The
key results of this Expos\'e are: (1) a universal characterization of the
$T$-$\infty$-category of $T$-objects in any $\infty$-category, (2) the
existence of an internal Hom for $T$-$\infty$-categories, and (3) a
parametrized Yoneda lemma.
