  The critical behavior of a three real parameter class of solutions of the
sixth Painlev\'e equation is computed, and parametrized in terms of monodromy
data of the associated $2\times 2$ matrix linear Fuchsian system of ODE. The
class may contain solutions with poles accumulating at the critical point. The
study of this class closes a gap in the description of the transcendents in one
to one correspondence with the monodromy data. These transcendents are reviewed
in the paper. Some formulas that relate the monodromy data to the critical
behaviors of the four real (two complex) parameter class of solutions are
missing in the literature, so they are computed here. A computational procedure
to write the full expansion of the four and three real parameter class of
solutions is proposed.
