This is a monograph on the fluctuational theory of superconductivity. The theory was originally developed by M. A. Savchenko in 1964 in response to the work of B. T. Matthias, the discoverer of superconductive compounds. Further development of the theory led to the prediction of the existence of high-temperature superconductors among magnetic and nonmagnetic compounds of rare-earth metals, ceramics, and polymers. In 1987 this prediction was experimentally verified by the discovery of high-Tc superconducting rare-earth metal oxides by I. Bednorz and K. Muller. To date, this is the only account...