Modern Geometry. Pt. 1. the Geometry of Surfaces, Transformation Groups, and Fields

Part I. The geometry of surfaces, transformation groups, and fields. This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in terminology acceptable to physicists.