Abstract: Linear space, linear functional and dual space are introduced. Based on this, tensor is defined mathematically as a multilinear functional, with bilinear form as an example. In addition, as a special case of bilinear form, inner product renders a co-vector interpretation of vector itself. Now setting all the linear spaces that vectors and co-vectors reside as \mathbbR^n\hspace0.25em\left(n=\mathrm2,3\right), the afore-defined tensor becomes that commonly used in the theory of continuum, viz, an entity that changes its coordinates/components according to certain given rules under coordinate transform of \mathbbR^n. Tensor product, contraction, dot product and double dot product are also explained.