  For every smooth complex projective variety $W$ of dimension $d$ and
nonnegative Kodaira dimension, we show the existence of a universal constant
$m$ depending only on $d$ and two natural invariants of the very general fibres
of an Iitaka fibration of $W$ such that the pluricanonical system $|mK_W|$
defines an Iitaka fibration. This is a consequence of a more general result on
polarized adjoint divisors. In order to prove these results we develop a
generalized theory of pairs, singularities, log canonical thresholds,
adjunction, etc.
