  We present microscopic derivation of the relativistic hydrodynamics (RHD)
equations directly from mechanics omitting derivation of kinetic equation. We
derive continuity equation and energy-momentum conservation law. We also derive
equation of evolution of particles current. In non-relativistic hydrodynamics
equation of particles current evolution coincide with the equation of momentum
evolution, the Maxwell's equations contain concentration and electric current
(which proportional to the particles current), so, to get a close set of
equations we should have equations of evolution of the concentration and the
particles current. Evolution of the particles current depends on the electrical
and magnetic fields. Thus, we obtain the set of the RHD equations as the set of
the continuity equation, the equation of particles current and the Maxwell
equations. This approximation does not require to include the evolution of
momentum and allows to consider physical problems. Certainly, particles current
evolution equation contains some new functions which we can express via
concentration and particles current or we can derive equation for this
functions, and, thus, get to more general approximation. This approximation
also developed and discussed in this paper.
