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Several problems are considered in this review. Using our dipole wave theory of diffraction the analytical formulas for diffraction from a narrow ring for different polarization were obtained. They were used in the new wave numerical model of an open resonator. A number of parameters of mode formation were investigated. It was shown that multipass geometrical “modes” win in competition with single pass Laguerre-Gaussian (LG) non-main modes during the relaxation oscillations. A method has been suggested for description of the azimuthally (A) and radially (R) polarized modes that excludes any inherent contradictions and unjustified approximations. It allows the analytical calculation of the field components for these modes, including the longitudinal one. Generation of high power beams with axial symmetric polarization in stable resonator of industrial CO2-laser with diffraction gratings has been realized. The transformation of azimuthally polarized mode to R-polarized mode was demonstrated. R-polarized beam was successfully used for cutting metal. The principal scheme based on a modified Sagnac interferometer was proposed and investigated experimentally. This external cavity technique was used for generation of R- and A-polarized laser beam.