  Baryogenesis via leptogenesis is an attractive scenario that links the
physics of right handed neutrino sector with the low energy neutrino data. In
the light of current neutrino oscillation data we studied the bound on the mass
scale ($M_1$) of lightest right handed neutrino ($N_1$) as well as their mass
hierarchy ($M_2/M_1$ and $M_3/M_1$) from the leptogenesis constraint which we
discussed in two different parts of the thesis. In part-I, we studied the
canonical leptogenesis in a {\it thermal} scenario and hence the bound on
$M_1$. It is shown that the mass scale of $N_1$ must satisfy the constraint
$M_1\geq 10^8$ GeV in order to produce the adequate lepton asymmetry. We then
led to propose a model where this bound can be relaxed to TeV scale. In
part-II, we studied the formation and evolution of topological defects which
are non-thermal objects and are expected to be formed during the early Universe
phase transitions. In particular, we considered $B-L$ cosmic strings and their
effect on leptogenesis and hence the bound on the mass scale of $N_1$. It is
shown that for the $B-L$ symmetry breaking scale $\eta_{B-L}>10^{11}$GeV, in
certain parameter space, the cosmic strings make a more dominant contribution
than thermal leptogenesis.
