The LOw Frequency ARay (LOFAR) is a multipurpose radio -antenna array aimed to detect radio signals in the 10 - 240 MHz frequency range, covering a large surface in Northern Europe with a higher density in the Northern Netherlands. Radio emission in the atmosphere is produced by cosmic -ray induced air showers through the interaction of charged particles with the Earth magnetic field. The detection of radio signals allows to reconstruct several properties of the observed cascade. We review here all important results achieved in the last years. We proved that the radio -signal distribution at ground level is described by a two-dimensional pattern, which is well fitted by a double Gaussian function. The radio -signal arrival time and polarization have been measured, thus providing additional information on the extensive air shower geometry, and on the radio emission processes. We also showed that the radio signal reaches ground in a thin, curved wavefront which is best parametrized by a hyperboloid shape centred around the shower axis. Radio emission has also been studied under thunderstorm conditions and compared to fair weather conditions. Moreover, by using a hybrid reconstruction technique, we performed mass composition measurements in the energy range 10(17) - 10(18) eV.