  In this thesis we work with Khovanov homology of links and its
generalizations, as well as with the homology of graphs. Khovanov homology of
links consists of graded chain complexes which are link invariants, up to chain
homotopy, with graded Euler characteristic equal to the Jones polynomial of the
link. Hence, it can be regarded as the "categorif\mbox{}ication" of the Jones
polynomial. \indent We prove that the f\mbox{}irst homology group of positive
braid knots is trivial. Futhermore, we prove that non-alternating torus knots
are homologically thick. In addition, we show that we can decrease the number
of full twists of torus knots without changing low-degree homology and
consequently that there exists stable homology for torus knots. We also prove
most of the above properties for Khovanov-Rozansky homology. \indent Concerning
graph homology, we categorify the dichromatic (and consequently Tutte)
polynomial for graphs, by categorifying an inf\mbox{}inite set of its
one-variable specializations. We categorify explicitly the one-variable
specialization that is an analog of the Jones polynomial of an alternating link
corresponding to the initial graph. Also, we categorify explicitly the whole
two-variable dichromatic polynomial of graphs by using Koszul complexes.
  \textbf{Key-words:} Khovanov homology, Jones polynomial, link, torus knot,
graph, dichromatic polynomial
