The purpose of this talk is to present new constructive results on Serre's reduction of
determined/overdetermined/underdetermined linear functional systems. Serre's reduction aims at finding
an equivalent presentation of a linear functional system which contains fewer equations and unknowns.
We shall explain why this problem can be reduced to the case where the equivalent system
contains only one equation. The different results, developed within a module-theoretic approach in collaboration
with M. S. Boudellioua (Sultan Qaboos University, Oman), are implemented in an OreModules package called Serre
developed in collaboration with T. Cluzeau (ENSIL, XLIM, University of Limoges, France). The different results
will be illustrated with explicit examples coming from control theory and engineering sciences.

Keywords: Serre's reduction, linear functional systems, finite presentations of modules, Baer's extensions,
extension modules, projective and free modules, Quillen-Suslin and Stafford theorems.