  In this paper, we show that the B\"acklund transformations of Painlev\'e
equations come from birational maps of rational surfaces constructed by Okamoto
as the spaces of initial conditions.
  The simultaneous resolutions of rational double points of the families of
rational surfaces give rise to flops which are origins of symmetry groups of
Painlev\'e equation. Moreover we point out that Kodaira--Spencer theory of
deformations of rational surfaces explains a geomrtric meaning of Painlev\'e
equations.
