The method of Groebner bases provides a uniform frame for the algorithmic solutions of quite some fundamental problems in algebraic geometry (commutative algebra) and in many other areas of mathematics that can be formulated in terms of sets of multivariate polynomials. Examples of problems that can be solved by Groebner bases are systems of polynomial equations over fields, linear diophantine equations over the ring of multivariate polynomials, computation in residue class rings modulo polynomial ideals, and the construction of bases for sets of polynomials that vanish on given polynomials. The Groebner bases method is now available in most of the current mathematical software systems like Mathematica, Maple, etc. and is also the main mathematical engine behind specialized systems for algebraic geometry like Macaulay, CoCoA and Singular.

In the talk, we will provide an easy introduction to the theory of Groebner bases and its applications. No prerequisites other than some elementary mathematics will be needed.