The traditional approach to the design of multi-layer optical coatings assumes setting the initial structure of coating, then the iteration procedure of direct operator to solving the problem of calculating the spectral characteristics of coatings by optimizing the parameters of this structure: number of layers, the refractive indices of the layers and their thickness. This procedure imposes additional restrictions on the parameters of the layers. In the monograph a new approach to the synthesis of the layered structure is described: the solution of the inverse problem when the layered structure is a result of applying the inverse operator for a given spectral characteristic. The book contains numerous examples of the synthesis of layered structures that differ from those obtained using traditional design methods. Monograph should be seen as complementary to existing books on optical coatings. It is useful not only for specialists in optics of thin-layer coatings, but interesting to experts in the related fields: microwave technology, acoustics, and nano-electronics.