Non-Euclidean geometry

The reader is offered a book by the famous German mathematician F. Klein (1849-1925). The first part extensively covers the basics of projective geometry and the theory of projective transformations, necessary for understanding the subsequent sections of the book. It then shows how concepts of Euclidean geometry can be introduced into projective geometry, describes the relationships connecting elliptic and hyperbolic geometries with Euclidean geometry, and studies the properties of non-Euclidean geometries. The third part describes the history and applications of non-Euclidean geometry, its relationship to other areas of mathematics. Recommended for university students - future mathematicians, as well as graduate students and specialists.