This book reviews the computer synthesis of diffractive optical elements (DOE) used for transforming laser radiation and investigating the properties of the wave fields produced. Methods for solving inverse problems of geometrical optics, scalar diffraction theory and electromagnetic theory of diffraction are discussed. Special attention is given to the difference methods of solving the Maxwell equations, finite and boundary elements for solving integral optics equations and connected waves for calculating diffraction in periodic structures. Topics include DOE forming self-reproducing laser beams used for handling micro-objects, DOE on diamond films used for transformation of powerful laser radiation and multi-order and spectral DOE used for simultaneous separation and focusing.