The subject to study is first of all fine films of semiconductors, as the movement of electrons and holes are quantized with respect to the degenerated direction. As a result the system becomes quasi-two-dimensional one. The same situation appears near the flat boundary of massive body due to the quantization of electron movement in potential well. The energy-band structure and external fields are additional problems in the investigation, so the accurate description of equilibrium and kinetic properties of quasi-two-dimensional electrons requires using different fields of modern theoretical physics. Experiments now allow to create solid body structures with electrons confined in one, two or even three dimensions. This structures turn out to have unique properties, so they are candidates to be used in microelectronics in future. Besides the studying in this domain affects on general developing of many-electron systems and forces us to reinterpret some theoretical suppositions.