  All knots in $R^3$ possess Seifert surfaces, and so the classical
Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in
a contact structure on $R^3$ can be defined. The definitions extend easily to
null-homologous knots in any $3$-manifold $M$ endowed with a contact structure
$\xi$. We generalize the definition of Seifert surfaces and use them to define
these invariants for all Legendrian knots, including those that are not
null-homologous, in a contact structure on the $3$-torus $T^3$. We show how to
compute the Thurston-Bennequin and rotation invariants in a tight oriented
contact structure on $T^3$ using projections.
