We present more than three years of observations at different frequencies, from radio to high-energy γ-rays, of the Narrow-Line Seyfert 1 (NLS1) Galaxy PMN J0948 + 0022 (z = 0.585). This source is the first NLS1 detected at energies above 100 MeV and therefore can be considered the prototype of this emerging new class of γ-ray emitting active galactic nuclei (AGN). The observations performed from 2008 August 1 to 2011 December 31 confirmed that PMN J0948 + 0022 generates a powerful relativistic jet, which is able to develop an isotropic luminosity at γ-rays of the order of 1048 erg s-1, at the level ofpowerful quasars. The evolution of the radiation emission of this source in 2009 and 2010 followed the canonical expectations of relativistic jets with correlated multiwavelength variability (γ-rays followed by radio emission after a few months), but it was difficult to retrieve a similar pattern in the light curves of 2011. The comparison of γ-ray spectra before and including 2011 data suggested that there was a softening of the high-energy spectral slope. We selected five specific epochs to be studied by modelling the broad-band spectrum, which are characterised by an outburst at γ-rays or very low/high flux at other wavelengths. The observed variability can largely be explained by changes in the injected power, the bulk Lorentz factor of the jet, or the electron spectrum. The characteristic time scale of doubling/halving flux ranges from a few days to a few months, depending on the frequency and the sampling rate. The shortest doubling time scale at γ-rays is 2.3 ± 0.5 days. These small values underline the need of highly sampled multiwavelength campaigns to better understand the physics of these sources.
