ABSTRACT
This chapter is devoted to tensor products of vector spaces and related topics such as the symmetric and exterior algebras. The term, tensor product, arises from its applications in differential geometry where it may be applied to the tangent or cotangent space of a manifold, but its utility is ubiquitous throughout mathematics. For example, in group theory, the tensor product is used to construct group representations. In other algebraic contexts, the tensor product is used to extend the base field of a vector space, for example, from the field of real numbers to the field of complex numbers.
