  Some applications of the odd Poisson bracket developed by Kharkov's theorists
are represented, including the reformulation of classical Hamiltonian dynamics,
the description of hydrodynamics as a Hamilton system by means of the odd
bracket and the dynamics formulation with the Grassmann-odd Lagrangian. Quantum
representations of the odd bracket are also constructed and applied for the
quantization of classical systems based on the odd bracket and for the
realization of the idea of a composite spinor structure of space-time. At last,
the linear odd bracket, corresponding to a semi-simple Lie group, is introduced
on the Grassmann algebra.
