Correspondence S.V. Kovalevskaya with the famous Swedish mathematician, founder of the journal "Acta mathematica" G. Mittag-Leffler, contains 88 letters from Mittag-Leffler and more than 400 letters and notes from Kovalevskaya. It is stored in the Mittag-Leffler archive in Dürsholm (Sweden). This publication publishes all letters and about half of the notes translated into Russian. The correspondence reflects various aspects of the life and work of Kovalevskaya and Mittag-Leffler: mathematics classes, scientific relations with scientists from different countries, statements on science, politics, literature, there are characteristics of many contemporary cultural figures. The publication is designed for readers interested in the problems of science of the XIX century.