At all redshifts much of galaxy properties depend on the IMF, including mass-to-light ratios, derived galaxy masses and star formation rates, the rate of the luminosity evolution of the constituent stellar populations, the metal enrichment, and so on . With so many important issues at stake, we still debate as to whether the IMF is universal, that is, the same in all places and at all cosmic times, or whether it depends on local conditions such as the intensity of star formation (starburst vs. steady star formation), or on cosmic time, for example, via the temperature of the microwave background. As is well known, we do not have anything close to a widely accepted theory of the IMF, and this situation is likely to last much longer than desirable. Again, star formation is an extremely complex (magneto)hydrodynamical process, indeed much more complex than stellar convection or red giant mass loss, for which we already noted the absence of significant theoretical progress over the last 40-50 years. Thus, the IMF is parametrized for example., as one or more power laws or as a lognormal distribution, and the parameters are fixed from pertinent observational constraints. Wherever the IMF has been measured from statistically significant stellar counts, a Salpeter IMF has been found, that is, (M) M -s, with s = 1 + x 2.35, however with a flattening to s 1.3 below ~ 0.5 M. Specifically, where possible, this has been proved for stellar samples including the solar vicinity, open and globular clusters in the Galaxy and in the Magellanic Clouds, actively starbursting regions, as well as the old galactic bulge. Nevertheless, this does not prove the universality of the IMF, as - with one exception - more extreme environments have not been tested yet in the same direct fashion. The exception is represented by the very center the of the Milky Way, in the vicinity of the supermassive black hole, a very extreme environment indeed, where very massive stars seem to dominate the mass distribution. In this chapter we discuss a few aspects of the IMF, using some of the stellar population tools that have been illustrated in the previous chapters, and exploring how specific integral properties of stellar populations depend on the IMF slope in specific mass intervals. In particular, the dependence on the IMF of the mass-to-light ratio of stellar populations is illustrated, along with its evolution as stellar populations passively age. Then the M/L ratios of synthetic stellar populations, and their time evolution, are compared to the dynamical M/L ratios of local elliptical galaxies, as well as to that of ellipticals up to redshift ~ 1 and beyond. These comparisons allow us to set some constraint on the low-mass portion of the IMF, from ~ 0.1 to ~ 1.4 M. A strong constraint of the IMF slope from ~ 1 M up to ~ 40 M and above is then derived from considering the metal content of clusters of galaxies together with their integrated optical luminosity.