We describe an experimental implementation of Groebner bases in the frame of the new software system Theorema. We use the functor construct of Theorema for establishing an abstract approach to Groebner bases theory based on the idea of "reduction rings". This approach promises to provide new insight into the basic mechanism of the Groebner bases approach. At the same time, in the talk, the example of Groebner bases theory will provide motivation for conceiving the Theorema software systems as a natural extension of current mathematical software systems like Mathematica into the direction of offering a common frame for future formal - algorithmic and nonalgorithmic - mathematics and mathematical knowledge management.

The talk will consist of a live demo of how to program and compute in Theorema.