This first volume of a three-part series introduces modern geometry, focusing on its applications in mathematics and theoretical physics. It covers tensors, differential calculus, and geometric field theory, presented in clear language suitable for physicists. The second edition features significant revisions.
This book discusses the evolution of university-level geometry education, highlighting the shift from classical differential geometry to the inclusion of Riemannian geometry and topology. It outlines the development of a modernized curriculum at Moscow State University, emphasizing essential topics like tensor theory and geodesics for practical applications in mathematics.