Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of 2 variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more.
Here's a sample of other books in this Dover category
Introduction to Vectors and Tensors: Second Edition--Two Volumes Bound as One by Ray M. Bowen, C.-C. Wang Convenient single-volume compilation of two texts offers both introduction and in-depth survey. Geared toward engineering and science students rather than mathematicians, it focuses on physics and engineering applications. 1976 edition.
Vectors and Their Applications by Anthony J. Pettofrezzo Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of 2- and 3-dimensional space.
