  The Carroll group was originally introduced by Levy-Leblond [1] by
considering the limit of the Poincar\'e group as $c\to0$. In this paper an
alternative definition, based on the geometric properties of a non-Minkowskian,
non-Galilean but nevertheless boost-invariant, space-time structure is
proposed. A "duality" with the Galilean limit $c\to\infty$ is established. Our
theory is illustrated by Carrollian electromagnetism.
