The present invention provides two ways to form a special permeability discontinuity unit inside every sub-lens of a multi-axis magnetic lens, which either has a simpler configuration or has more flexibility in manufacturing such as material selection and mechanical structure. Accordingly several types of multi-axis magnetic lens are proposed for various applications. One type is for general application such as a multi-axis magnetic condenser lens or a multi-axis magnetic transfer lens, another type is a multi-axis magnetic non-immersion objective which can require a lower magnetomotive force, and one more type is a multi-axis magnetic immersion objective lens which can generate smaller aberrations. Due to using permeability-discontinuity units, every multi-axis magnetic lens in this invention can also be electrically excited to function as a multi-axis electromagnetic compound lens so as to further reduce aberrations thereof and/or realize electron beam retarding for low-voltage irradiation on specimen.