  The notions of "motion" and "conserved quantities", if applied to extended
objects, are already quite non-trivial in Special Relativity. This contribution
is meant to remind us on all the relevant mathematical structures and
constructions that underlie these concepts, which we will review in some
detail. Next to the prerequisites from Special Relativity, like Minkowski space
and its automorphism group, this will include the notion of a body in Minkowski
space, the momentum map, a characterisation of the habitat of globally
conserved quantities associated with Poincar\'e symmetry -- so called
Poincar\'e charges --, the frame-dependent decomposition of global angular
momentum into Spin and an orbital part, and, last not least, the likewise
frame-dependent notion of centre of mass together with a geometric description
of the Moeller Radius, of which we also list some typical values. Two
Appendices present some mathematical background material on Hodge duality and
group actions on manifolds. This is a contribution to the book: "Equations of
Motion in Relativistic Gravity", edited by Dirk Puetzfeld and Claus
Laemmerzahl, to be published by Springer Verlag.
