Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts Tristan Needham is an English-language textbook aimed at differential geometry and forms. This book is suitable for students and professionals looking for deeper insight within these mathematical disciplines.
The work offers a visual and intuitive approach to differential geometry and uses 235 hand-drawn diagrams. In the first four parts, geometry is at the center, including, among other things, four proofs of the Global Gauss-Bonnet Theorem, a geometric proof of Gauss' Theorema Egregium, and an extensive treatment of the Riemann curvature tensor and Einstein's field equations.
The fifth part introduces differential forms from a geometric perspective and covers topics such as integration theory, Maxwell's equations in terms of 2-forms, de Rham cohomology, and Cartan’s methods. This makes the book a valuable source in the study of geometry and forms, with applications in both topology and mathematical physics.