This chapter study mathematical model of multi-layer metasurface. Firstly, based on the tangential field and normal wave vector, obliquely incident waves can be treated as normally incident, thereby enabling the establishment of a tangential network transmission theory for reflective metasurfaces. As the number of layers increases in a transmissive metasurface, it is difficult to sum the matrix series. Thereby, four-dimensional characteristic matrix theory is proposed for multi-layer transmissive metasurfaces. Furthermore, this chapter focuses on the metasurface polarization converters. Using the tangential network transmission theory, the total reflection matrix can be related to the electrical parameters of the unit structure, among other factors-is derived. After obtaining the analytical expressions of the electrical parameters, the geometric parameters of the unit structure can be analytically solved design. Finally, by combining anisotropic metal structures of different sizes, the resonant frequencies of the metasurface are extended, thereby broadening the polarization conversion bandwidth.