In many branches of science and engineering where mathematics is used, the resolution of a problem coming from practice is often reduced to the search of a solution for a system of (algebraic or differential) equations modelling the considered problem. From our point of view, to solve a polynomial system of equations is to rewrite it (i.e., to present it in a different form) in such a way that some ‘nontrivial’ information about its solutions can be derived from this new presentation. The information mentioned above can be related to the existence or non-existence of complex or real solutions, to the number of real or complex solutions, to the approximation of one or several solutions, etc.