V. I. Keilis-Borok (1921-2013) is one of the founders of computational seismology and mathematical geophysics and a pioneer in advance predictions of extreme events in complex systems, including earthquakes, economic recessions, outcomes of elections, surges of unemployment, and crime waves. This book overviews over fifty years of work by V. I. Keilis-Borok and his group on developing successful algorithms for prediction of extreme events in nature and society.