  The sixth Painlev\'e equation is hiding extremely rich geometric structures
behind its outward appearance. This article tries to give as a total picture as
possible of its dynamical natures, based on the Riemann-Hilbert approach
recently developed by the authors, using various techniques from algebraic
geometry. A good part of the contents is extended to Garnier systems, while
this article is restricted to the original sixth Painlev\'e equation.
