This is a short introduction to the basics of the theory of normed tensor products. The m-fold tensor product of linear spaces is defined through the universal property. If the involved spaces are normed, then the projective and injective norms on the tensor product are. Basic properties are given: the metric mapping property and their relationship with continuous linear mappings. The symmetric m-fold tensor product and the symmetric projective and injective norms are defined analogously. These are related to the m-homogeneous polynomials.