Many of us have heard that modern science has long ago called into question the basic postulates of Euclidean geometry.  But what exactly theories came to replace the classical doctrine?  The only thing that comes to mind is Einstein’s popular theory of relativity.  In fact, there are many more such revolutionary ideas and hypotheses.  Minkowski space, hyperbolic geometry of Lobachevsky and Bolyai, elliptic geometry of Riemann and other interesting ways of describing the world around us belong to the group of so-called non-Euclidean geometries.  How do parallel lines intersect?  In what case can the sum of the interior angles of a triangle be greater than 180°?  You will find answers to these and many other questions in this book.