We present the results from adaptive optics ( AO ) assisted imaging in the K _ { \mathrm { s } } band of an area of 15 \textrm { arcmin } ^ { 2 } for SWAN ( Survey of a Wide Area with NACO ) . We derive the high resolution near-IR morphology of \sim 400 galaxies up to K _ { \mathrm { s } } \sim 23.5 in the first 21 SWAN fields around bright guide stars , carefully taking into account the survey selection effects and using an accurate treatment of the anisoplanatic AO PSF . The detected galaxies are sorted into two morphological classes according to their Sérsic index . The extracted morphological properties and number counts of the galaxies are compared with the predictions of different galaxy formation and evolution models , both for the whole galaxy population and separately for late-type and early-type galaxies . This is one of the first times such a comparison has been done in the near-IR , as AO observations and accurate PSF modeling are needed to obtain reliable morphological classification of faint field galaxies at these wavelengths . For early-type galaxies we find that a pure luminosity evolution model , without evidence for relevant number and size evolution , better reproduces the observed properties of our K _ { \mathrm { s } } -selected sample than current semi-analytic models based on the hierarchical picture of galaxy formation . In particular , we find that the observed flattening of elliptical galaxy counts at K _ { \mathrm { s } } \sim 20 is quantitatively in good agreement with the prediction of the pure luminosity evolution model that was calculated prior to the observation . For late-type galaxies , while both models are able to reproduce the number counts , we find some hints of a possible size growth . These results demonstrate the unique power of AO observations to derive high resolution details of faint galaxies ’ morphology in the near-IR and drive studies of galaxy evolution .