  In the present paper a description of a problem of point vortices on a plane
and a sphere in the "internal" variables is discussed. The hamiltonian
equations of motion of vortices on a plane are built on the Lie-Poisson
algebras, and in the case of vortices on a sphere on the quadratic Jacobi
algebras. The last ones are obtained by deformation of the corresponding linear
algebras. Some partial solutions of the systems of three and four vortices are
considered. Stationary and static vortex configurations are found.
