There are many peoples who claim to invent some aspects of Grobner theory. The major step was taken by B. Buchberger in the mid of sixties. He formulated the concept of Grobner basis and extends the suggestions of his advisor W. Grobner. The introduction of Grobner basis is analogous to the introduction of i as a solution of the equation x² + 1 = 0.Similarly for solving the Ideal Membership problem in polynomial rings the Grobner basis for ideal was introduced. But one can see that the vast arrays of other problems are also solved by using Grobner basis.