The authors describe a general approach to group-invariant solutions of partial differential equations. They introduce the concept of a ''weak symmetry group'' of a system of partial differential equations and show how, in principle, to construct group-invariant solutions for any group of transformations by reducing the number of variables in the system. But the paper also contains the result that every solution of a given system can be found using the reduction method with some weak symmetry group. The theoretical considerations are illustrated by a number of examples, including the heat equation, a nonlinear wave equation and a version of the Boussinesq equation.