  A theory of electromagnetic (EM) wave scattering by many small particles of
an arbitrary shape is developed. The particles are perfectly conducting or
impedance. For a small impedance particle of an arbitrary shape an explicit
analytical formula is derived for the scattering amplitude. The formula holds
as $a\to 0$, where $a$ is a characteristic size of the small particle and the
wavelength is arbitrary but fixed. The scattering amplitude for a small
impedance particle is shown to be proportional to $a^{2-\kappa}$, where
$\kappa\in [0,1)$ is a parameter which can be chosen by an experimenter as
he/she wants. The boundary impedance of a small particle is assumed to be of
the form $\zeta=ha^{-\kappa}$, where $h=$const, Re$h\ge 0$. The scattering
amplitude for a small perfectly conducting particle is proportional to $a^3$,
it is much smaller than that for the small impedance particle. The many-body
scattering problem is solved under the physical assumptions $a\ll d\ll
\lambda$, where $d$ is the minimal distance between neighboring particles and
$\lambda$ is the wavelength. The distribution law for the small impedance
particles is $\mathcal{N}(\delta)\sim\int_{\delta}N(x)dx$ as $a\to 0$. Here
$N(x)\ge 0$ is an arbitrary continuous function that can be chosen by the
experimenter and $\mathcal{N}(\delta)$ is the number of particles in an
arbitrary sub-domain $\Delta$. It is proved that the EM field in the medium
where many small particles, impedance or perfectly conducting, are distributed,
has a limit, as $a\to 0$ and a differential equation is derived for the
limiting field. On this basis the recipe is given for creating materials with a
desired refraction coefficient by embedding many small impedance particles into
a given material.
