Laser Beam Mode Selection by Computer Generated Holograms brings attention to a new class of optical elements called modans, with applications in laser and fiber optics. Separation of the transverse modes by modans is discussed in close analogy to well-known effects of color separation by diffraction gratings. The book describes the basic questions of digital holography in the recording of complex wavefronts on phase-only media, binary coding cells, multilevel computer-generated holograms, quantization and sampling, image reconstruction, and computer generation of multifocal and multibeam holograms. This collective effort summarizes 12 years of scientific activities in the development of diffractive optical elements and provides considerable material never before published. An interesting appendix dedicates itself to mathematical proof of optimal properties of orthogonal base-functions and eigenfunctions.