Definition of vectors and discussion of algebraic operations on vectors leads to concept of tensor and algebraic operations on tensors. Also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time, more. Concise, eminently readable text. Worked out problems and solutions.
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.
Vector Analysis by Homer E. Newell, Jr. This text combines the logical approach of a mathematical subject with the intuitive approach of engineering and physical topics. Applications include kinematics, mechanics, and electromagnetic theory. Includes exercises and answers. 1955 edition.