  A reduction of the Maxwell's system to a Fredholm second-kind integral
equation with weakly singular kernel is given for electromagnetic (EM) wave
scattering by one and many small bodies. This equation is solved asymptotically
as the characteristic size of the bodies tends to zero. The technique developed
is used for solving the many-body EM wave scattering problem by rigorously
reducing it to solving linear algebraic systems, completely bypassing the usage
of integral equations. An equation is derived for the effective field in the
medium, in which many small particles are embedded. A method for creating a
desired refraction coefficient is outlined.
