This essay sets out the history of mathematics until the beginning of the 19th century. Written by a team of Soviet scientists, this work reflects the basic general principles of the Soviet school of historians of mathematics. The progressive movement of mathematics is seen not only as the process of creating more and more advanced ideas and methods for the study of spatial forms and quantitative relations of the real world, but also as a social phenomenon. Once the mathematical structures that have already arisen always develop to one degree or another independently, but this self-development occurs in the conditions and on the basis of the practical activities of people and is determined, sometimes directly, sometimes ultimately, by the needs of society. The work is divided into three volumes. The first is devoted to antiquity (the first part), the Middle Ages and the Renaissance (the second part), the second - XVII century. and the third - XVIII century. Since the book is intended for a wide range of readers familiar with mathematics in a volume not exceeding the course of higher technical schools, we had to leave aside many details that those who wish can familiarize themselves with the literature provided at the end of each volume.