We present theoretical studies on the collective optical response of symmetric configurations of metallic nanoparticles. We show that within the electrostatic approximation, the surface plasmon resonance of these symmetric multiparticle systems can be expressed as symmetry-adapted linear combinations of the plasmon modes of each particle of the ensemble, closely resembling the situation encountered in molecular systems. By making use of group theoretical arguments, we show that such linear combinations can be written down by simple geometrical considerations through the use of point group character tables, without using extensive numerical computations. Furthermore, we apply this formalism to study the coupling of hierarchical arrays containing a large number of nanoparticles. This theory thus provides an intuitive and formal approach for the rational design of plasmonic nanostructures.