Groebner bases algorithm: an introduction

Groebner Bases is a technique that provides algorithmic solutions to a variety of problems in Commutative Algebra and Algebraic Geometry. In this introductory tutorial the basic algorithms as well as their generalization for computing Groebner basis of a set of multivariate polynomials are presented. The Groebner basis technique is applied to solve systems of polynomial equations in several variables. This technical report investigates this application.