  In this thesis we define and study a categorification of the sl(N)-link
polynomial using foams, for N\geq 3.
  For N=3 we define the universal sl(3)-link homology, using foams, which
depends on three parameters and show that it is functorial, up to scalars, with
respect to link cobordisms. Our theory is integral. We show that tensoring it
with Q yields a theory which is equivalent to the rational universal
Khovanov-Rozansky sl(3)-link homology.
  For N\geq 4 we construct a rational theory categorifying the sl(N)-link
polynomial using foams. Our theory is functorial, up to scalars, with respect
to link cobordisms. To evaluate closed foams we use the Kapustin-Li formula. We
show that for any link our homology is isomorphic to the Khovanov-Rozansky
homology. We conjecture that the theory is integral and we compute the
conjectured integral sl(N)-link homology for the (2,m)-torus links and show
that it has torsion of order N.
