  This review is made of two parts which are related to Poincar\'e in different
ways. The first part reviews the work of Poincar\'e on the Theory of (Special)
Relativity. One emphasizes both the remarkable achievements of Poincar\'e, and
the fact that he never came close to what is the essential conceptual
achievement of Einstein: changing the concept of time. The second part reviews
a topic which probably would have appealed to Poincar\'e because it involves
several mathematical structures he worked on: chaotic dynamics, discrete
reflection groups, and Lobachevskii space. This topic is the hidden role of
Kac-Moody algebras in the billiard description of the asymptotic behaviour of
certain Einstein-matter systems near a cosmological singularity. Of particular
interest are the Einstein-matter systems arising in the low-energy limit of
superstring theory. These systems seem to exhibit the highest-rank hyperbolic
Kac-Moody algebras, and notably E(10), as hidden symmetries.
