  The third, fifth and sixth Painlev\'e equations are studied by means of the
weighted projective spaces ${\mathbb C}P^3(p,q,r,s)$ with suitable weights
$(p,q,r,s)$ determined by the Newton polyhedrons of the equations. Singular
normal forms of the equations, symplectic atlases of the spaces of initial
conditions, Riccati solutions and Boutroux's coordinates are systematically
studied in a unified way with the aid of the orbifold structure of ${\mathbb
C}P^3(p,q,r,s)$ and dynamical systems theory.
