This undergraduate textual content presents an advent to the speculation of Cartesian tensors, defining tensors as multilinear features of path, and simplifying many theorems in a way that lends harmony to the topic. the writer notes the significance of the research of the constitution of tensors by way of spectral units of projection operators as a part of the very substance of quantum concept. He for this reason presents an ordinary dialogue of the topic, as well as a view of isotropic tensors and spinor research in the confines of Euclidean house. The textual content concludes with an exam of tensors in orthogonal curvilinear coordinates. quite a few examples illustrate the final conception and point out definite extensions and purposes. 1960 edition.