  We present the most accurate measurement to date of cosmological evolution of
the near-infrared galaxy luminosity function, from the local Universe out to
z~4. The analysis is based on a large and highly complete sample of galaxies
selected from the first data release of the UKIDSS Ultra Deep Survey.
Exploiting a master catalogue of K- and z-band selected galaxies over an area
of 0.7 square degrees, we analyse a sample of ~50,000 galaxies, all with
reliable photometry in 16-bands from the far-ultraviolet to the mid-infrared.
The unique combination of large area and depth provided by the Ultra Deep
Survey allows us to trace the evolution of the K-band luminosity function with
unprecedented accuracy. In particular, via a maximum likelihood analysis we
obtain a simple parameterization for the luminosity function and its
cosmological evolution, including both luminosity and density evolution, which
provides an excellent description of the data from z =0 up to z~4. We find
differential evolution for galaxies dependent on galaxy luminosity, revealing
once again the ``down-sizing behaviour'' of galaxy formation. Finally, we
compare our results with the predictions of the latest theoretical models of
galaxy formation, based both on semi-analytical prescriptions, and on full
hydrodynamical simulations.
