Groebner bases and solving systems of polynomial equations

The report will be devoted to the modern algorithms for constructing special bases of the ideals in polynomial rings so called Groebner bases. This technique can be used for solving system of polynomial equations and give us information about manifold of solutions such as dimension of the manifold of solutions, Hilbert polynomial et al. Some generalizations of this technique for the differential and noncommutative cases and the case of the ideals in the ring of formal power series will be presented.