This book is about mathematics in Sweden between 1630 and 1950 - from S. Klingenstierna to M. Riesz, T. Carleman, and A. Beurling. It tells the story of how continental mathematics came to Sweden, how it was received, and how it inspired new results. The book contains a biography of Gosta Mittag-Leffler, the father of Swedish mathematics, who introduced the Weierstrassian theory of analytic functions and dominated a golden age from 1880 to 1910. Important results are analyzed and re-proved in modern notation, with explanations of their relations to mathematics at the time. The book treats Backlund transformations, Mittag-Leffler's theorem, the Phragmen-Lindelof theorem and Carleman's contributions to the spectral theorem, quantum mechanics, and the asymptotics of eigenvalues and eigenfunctions.