The Grobner Basis constitute a central axis in the theory of Computational Algebra. Its versatility and large number of applications have allowed these to be used for research in various branches of mathematics, such as Commutative Algebra, Algebraic Geometry, Graph Theory, Code Theory, Cryptography, to mention only some of them. The present document has an introductory purpose towards the Grobner basis, taking as reference some of its applications.