Semiconductor structures containing zero-dimensional objects — quantum dots — are the subject of intensive research worldwide. This monograph describes a detailed theory of the electronic band structure and optical properties of semiconductor quantum dots.The author provides a comprehensive description of an original approach based on a combination of the Fourier transform, the Green's function and plane-wave expansion techniques in the framework of multiband 8x8 kp theory. The calculated band structure, optical properties and device applications are analyzed in line with available experiments for a large number of realistic quantum dot structures and various combinations of materials, such as InGaN, GaN/AlN, ZnSe, InGaAs (including dots-in-the-well), ZnSe/CdSe, and lead salts.