Creating materials with a desired refraction coefficient Creating Materials with a Desired Refraction Coefficient provides a recipe for creating materials with a desired refraction coefficient and the many body wave scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated which when solved make the theory practically applicable. The Importance of a problem of producing a small particle with a desired boundary impedance is emphasized and inverse scattering with non over determined scattering data is considered.