The formation and evolution of clusters and proto-clusters of galaxies will be studied using unique diagnostic tools provided by the new pan-European radio telescope LOFAR and the APERTIF phased arrays on WSRT radio telescope. Combined with new ultra low frequency antennas (an extension to LOFAR here proposed), these new facilities will for the first time enable sensitive observations from the lowest possible frequencies accessible from the ground (~15 MHz) up to 1400 MHz. The guaranteed time projects (PI HR) to carry out ultra deep pointed observations and to survey the entire northern sky will be unique in terms of angular resolution, depth, and extremely large frequency range. This enables a coherent study of clusters of galaxies over the entire history of the universe up to the formation of the first proto-clusters.Studies of the associated shock waves produced by cluster mergers and the magnetic field properties of the cluster gas will constrain models of the formation of galaxy clusters.The large field of views of both LOFAR will enable the detection of radio emission from millions of star-forming galaxies up to z=2-3, at the epoch at which the bulk of galaxy formation is believed to have occurred. In combination with infrared surveys, the first significant sample of proto-clusters of galaxies will be obtained. This will enable the first complete study of the overall properties of proto-clusters and their galaxy contents.With LOFAR’s ability to pinpoint radio sources with extremely steep radio spectra, we will detect radio galaxies at unprecedented distances. As our previous radio and optical investigations have established that distant radio galaxies are often located in proto-clusters, the most distant LOFAR radio galaxies would be excellent targets to locate and study the first proto-clusters close to or even at the epoch of reionisation.