Tensors are generalizations of vectors. These manifestate as 1. * product of vector spaces 2. * product of linear maps 3. * multi-indexed arrangements of numbers or scalar functions In the first case we take two vector spaces , and construct a new one by mean of their basis: if V has as basic vectors and W has then is the vector space generated by the symbols which are all the linear combinations of pairs . In another hand, if we want to construct a bilinear map then we pick up a pair of covectors and then we manufacture defined via