  Let $X$ be a smooth complex projective algebraic variety of maximal Albanese
dimension. We give a characterization of $\kappa (X)$ in terms of the set
$V^0(X,\omega_{X})$ $:=\{P\in {\text{\rm Pic}}^0(X)|h^0(X, \omega_X \otimes P)
\ne 0\}$. An immediate consequence of this is that the Kodaira dimension
$\kappa (X)$ is invariant under smooth deformations. We then study the
pluricanonical maps $\phi_m:X -> \Bbb{P} (H^0(X,mK_X))$. We prove that if $X$
is of general type, $\phi_m$ is generically finite for $m\geq 5$ and birational
for $m\geq 5 \text{\rm dim} (X) +1$. More generally, we show that for $m\geq 6$
the image of $\phi_m$ is of dimension equal to $\kappa (X)$ and for $m\geq
6\kappa (X)+2$, $\phi_m$ is the stable canonical map.
