When dealing ‘with systems of just a few identical particles, it is easy to construct explicitly symmetric or antisymmetric wave functions. This can prove however to be a rather cumbersome task when studying systems with enormous numbers of identical particles, such as the electrons in a metal, or liquid He4. I would like therefore to describe a very elegant way of accounting for the symmetry of the states and the operators of systems of many identical particles, and illustrate its use in a few simple calculations.