  Landau hydrodynamics is a plausible description for the evolution of the
dense hot matter produced in high-energy heavy-ion collisions. We review the
formulation of Landau hydrodynamics to pave the way for its application in
high-energy heavy-ion collisions. It is found that Landau's rapidity
distribution needs to be modified to provide a better quantitative description.
In particular, the rapidity distribution in the center-of-mass system should be
more appropriately given as dN/dy \exp{\sqrt{y_b^2-y^2}}, where
y_b=\ln{\sqrt{s_NN}/m_p} is the beam nucleon rapidity, instead of Landau's
original result of dN/dy({Landau}) \exp{\sqrt{L^2-y^2}} where
L=\ln{\sqrt{s_NN}/2m_p}. The modified distribution is compared with the Landau
distribution and experimental data. It is found that the modified distribution
agrees better with experimental $dN/dy$ data than the Landau distribution and
it differs only slightly from the Landau Gaussian distribution
dN/dy(Landau-Gaussian) \exp{-y^2/2L}. Past successes of the Gaussian
distribution in explaining experimental rapidity data arises, not because it is
an approximation of the original Landau distribution, but because it is in fact
a close representation of the modified distribution.
