  In the first chapter we present new results related on monomial ideals of
Borel type. Also, we introduce a new class of monomial ideals, called
$\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we
extend several results to this new class.
  In the second chapter, we compute the generic initial ideal, with repect to
the reverse lexicographic order, of an ideal which define a complete
intersection of embedding dimension three with strong Lefschetz property and we
show that it is an almost reverse lexicographic ideal. This enable us to give a
proof for Moreno's conjecture in the case $n=3$ and characteristic zero. Also,
we prove that the $d$-component of the generic initial ideal, with respect to
the reverse lexicographic order, of an ideal generated by a regular sequence of
homogeneous polynomials of degree $d$ is revlex, in a particular, but
important, case.
