  Interactions of heavy Majorana neutrinos in the thermal phase of the early
universe may be the origin of the cosmological matter-antimatter asymmetry.
This mechanism of baryogenesis implies stringent constraints on light and heavy
Majorana neutrino masses. We derive an improved upper bound on the CP asymmetry
in heavy neutrino decays which, together with the kinetic equations, yields an
upper bound on all light neutrino masses of 0.1 eV. Lepton number changing
processes at temperatures above the temperature T_B of baryogenesis can erase
other, pre-existing contributions to the baryon asymmetry. We find that these
washout processes become very efficient if the effective neutrino mass
\tilde{m}_1 is larger than m_* \simeq 10^{-3} eV. All memory of the initial
conditions is then erased. Hence, for neutrino masses in the range from (\Delta
m^2_sol)^{1/2} \simeq 8*10^{-3} eV to (\Delta m^2_atm)^{1/2} \simeq 5*10^{-2}
eV, which is suggested by neutrino oscillations, leptogenesis emerges as the
unique source of the cosmological matter-antimatter asymmetry.
