This book will employ physical modeling and mathematical derivation to develop an analytical theory for electromagnetic metasurface, which aims to deepen physical mechanisms and lays a solid theoretical foundation for further research on metasurfaces. Firstly, the book presents the general description of metasurface boundary conditions and key calculation methods, Secondly, the book develops the network transmission theory for multi-layer metasurface structures, yielding mathematical model of metasurface-based polarization converters. Thirdly, the book establishes the electromagnetic theory of complementary metasurfaces at dielectric interfaces, overcoming limitations of existing Babinet principle applications. Fourthly, the book investigates the quantitative impact of dielectric interface on the metallic metasurface structures and extend the concept of effective dielectric constant. Fifthly, the book establishes the dispersion theory of gap waveguides, linking metasurface periodicity principles to waveguide dispersion characteristics and mode propagation behavior. Finally, the book focuses on the reciprocity principle for metasurface scattering coefficients. The book is intended for students and researchers who are interested in electromagnetic metasurface and electromagnetic theory.