Metasurfaces constitute a class of thin metamaterials, which  are used to control plane waves and surface waves, i.e. to   enable new radiation and guiding properties. Metasurfaces   can be employed for realizing highly customizable  EM devices  from microwave to optical frequencies. During   this course the background and theory of different types  of metasurfaces will be explained, as well as how to  implement these theoretical models in different numerical methods and practical designs. The work will be presented in relation to specific applications such as: controllable “smart” surfaces, new types of antennas, flat optics, devices for tailoring wavefronts, novel wave-guiding structures, directivity enhancement, reduction of far out sidelobes and tunable active metasurface structures.