The book is devoted to the life and work of the outstanding Russian mathematician and mechanic, academician A.M. Lyapunov (1857-1918), who developed a number of scientific areas that have not lost their significance today. The rigorous and general stability theory he created is recognized worldwide, and the methods Lyapunov developed are at the heart of most modern sustainability research. Using archival materials, the author recreates the life and career of A. M. Lyapunov against the background of the scientific life of Russia in the late XIX - early XX centuries, closely intertwined with the fate of his brothers - composer S. M. Lyapunov and academician-Slavist B. M. Lyapunov.