Ignacio Ferreras - September 26, 2014 On the initial mass function and the formation of massive galaxies The initial mass function (IMF) represents the distribution of stellar masses at birth. Although it is often considered a universal function, based on studies of nearby resolved populations, the physical conditions of the environment of star forming regions can vary widely from the inefficient, self-regulated star formation in dwarf galaxies to intense runaway bursts in the most massive systems. Over the past few years, the concept of a non-universal IMF has gained support thanks to spectroscopic evidence targeting line strengths that are specially sensitive to the presence of low-mass, main sequence stars. Following a similar trend as other fundamental stellar population properties such as age, metallicity or alpha-enhancement, the IMF of early-type galaxies appears to depend on the central velocity dispersion of the galaxy, towards an excess of low-mass stars in the cores of the most massive systems. The combined observational information suggests a qualitatively different mode of star formation in massive galaxies. Simple models of chemical enrichment lead to a time-dependent transition of this mode. I will present a review of the methods used to derive the trends, the uncertainties and systematics behind the modelling, and the consequences of such a scenario to our understanding of galaxy formation and star formation in extreme environments.