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.
Authored by a prestigious Fields medal winner, this book delves into advanced mathematical concepts while making them accessible to a broader audience. It combines rigorous theory with engaging examples, showcasing the beauty and intricacies of mathematics. Readers can expect to explore innovative ideas and applications that challenge conventional thinking, making it a valuable resource for both enthusiasts and professionals in the field. The author's unique insights and expertise illuminate the subject, fostering a deeper appreciation for mathematics.