This book introduces fundamental principles as well as applications of metasurfaces, i.e. electromagnetically thin structures manipulating EM wave propagation. The authors describe the precursors and history of metasurfaces before moving on to explore the physical insights that can be gained from the material parameters of the metasurface. They also present how to compute the fields scattered by a metasurface, with known material parameters, being illuminated by an arbitrary incident field, as well as how to realize a practical metasurface and relate it its material parameters to physical structures.The book finishes with a discussion of the future of the field.