The current work has described the new experimental method, Advanced Method of Transient Microwave Photoconductivity (AMTMP) and its capabilities to study the photoelectronic properties of semiconductors. AMTMP measures not only the effect proportional to the excess conduction band electrons ("photoconductivity" itself, related to the changes in the imaginary part of the complex dielectric constant), but also the changes in the real part of the complex dielectric constant ("photodielectric effect"). In a rigorous treatment of the complex dielectric constant changes in a microwave cavity general expressions relating the changes in complex dielectric constant to two experimentally measured quantities (change in the cavity quality factor and the shift of the resonance frequency) were derived. Based on this method it was possible to systematize basic types of excitations (free electrons, plasma, trapped electrons, excitons) as bound/non-bound states. To interpret the behavior of the kinetics in semiconductors having distributions of the localized states in the band gap the simulation approach based on solving numerically multiple trapping rate equations was developed. With this approach the major basic types of distributions (rectangular, linear, exponential, Gaussian) were explored thoroughly. We tested the method on various semiconductors: two types of polycrystalline CdSe thin films ( For SI GaAs we were able to separate the mobility changes from the concentration changes in the photoconductivity decays. We showed that to observe excess free electrons rather than trapped electrons dominate in the changes of the real part of the dielectric constant the material has to possess high mobility carriers and relatively low trap densities.