In the field of classical tensor algebra, there still exist a few concepts that have not been formulated by using concepts of multilinear algebra and analysis on manifolds. Hence, we have tried to reformulate some matters that arise in classical tensor analysis and a few others that we had identified and resolved. These being: the meaning of the equivalence of first order tensor with vector; the pull back and push forward structure, the structure of contraction of tensors, the inner product term, ds2 as a differential and the algebraic structure of relative tensors and tensor densities.