The paper proposes a novel approach to far-field optical imaging that surpasses the diffraction limit. The system, called the hyperlens, is designed to magnify subwavelength features and can be fabricated using existing metamaterial technologies in a cylindrical geometry. The key innovation lies in the use of strongly anisotropic metamaterials with opposite signs of the two permittivity tensor components, which enable the propagation of high-$k$ modes that would otherwise be evanescent in ordinary dielectrics. This allows the hyperlens to convert evanescent waves into propagating waves, facilitating their detection and processing in the far field. The device's cylindrical geometry ensures that subwavelength features are magnified beyond the diffraction limit, and simulations show that material losses do not appreciably degrade its performance. The hyperlens can be combined with an evanescent wave enhancer to further improve resolution, making it a promising tool for applications such as biological microscopy.The paper proposes a novel approach to far-field optical imaging that surpasses the diffraction limit. The system, called the hyperlens, is designed to magnify subwavelength features and can be fabricated using existing metamaterial technologies in a cylindrical geometry. The key innovation lies in the use of strongly anisotropic metamaterials with opposite signs of the two permittivity tensor components, which enable the propagation of high-$k$ modes that would otherwise be evanescent in ordinary dielectrics. This allows the hyperlens to convert evanescent waves into propagating waves, facilitating their detection and processing in the far field. The device's cylindrical geometry ensures that subwavelength features are magnified beyond the diffraction limit, and simulations show that material losses do not appreciably degrade its performance. The hyperlens can be combined with an evanescent wave enhancer to further improve resolution, making it a promising tool for applications such as biological microscopy.