  The metric jets, introduced in the first chapter, generalize the jets (at
order one) of Charles Ehresmann. In short, for a "good" map $f$ (said to be
"tangentiable" at $a$), we define its metric jet tangent at $a$ (composed of
all the maps which are locally lipschitzian at $a$ and tangent to $f$ at $a$)
called the "tangential" of $f$ at $a$, and denoted T$f_a$ (the domain and
codomain of $f$ being metric spaces).
  Furthermore, guided by the heuristic example of the metric jet T$f_a$,
tangent to a map $f$ differentiable at $a$, which can be canonically
represented by the unique continuous affine map it contains, we will extend, in
the second chapter, into a specific metric context, this property of
representation of a metric jet.This yields a lot of relevant examples of such
representations.
