Distribution functions of rotating galaxies : an integral field spectroscopy perspective The work done during the PhD studies has been focused on measurements of distribution functions of rotating galaxies using integral field spectroscopy observations. Throughout the main body of research presented here we have been using CALIFA (Calar Alto Legacy Integral Field Area) survey stellar velocity fields to obtain robust measurements of circular velocities for rotating galaxies of all morphological types. A crucial part of the work was enabled by well defined CALIFA sample selection criteria: it enabled reconstructing sample independent distributions of galaxy properties. In Chapter 2 we measure the distribution in absolute magnitude circular velocity space for a well defined sample of 199 rotating CALIFA galaxies using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early type galaxies. Our initial ...