The free rigid body dynamics is one of the typical solvable problems in classical analytical
mechanics. However, there are still plenty of interesting researches around this system from
modern mathematical points of view. This talk deals with some geometric aspects of the
free rigid body dynamics mainly on the basis of the speaker’s works with J.-P. Fran ̧coise and
I. Naruki. After a brief overview on the symplectic and Poisson geometric formulation of the
system, two associated elliptic fibrations are studied from algebro-geometric viewpoint and
the connection to the Birkhoff normal forms around equilibrium points is also explained.
Other geometric aspects of the dynamics, including some recent developments, are also
mentioned