The stellar initial mass function (IMF) is one of the cornerstones of modern astrophysics and its universality or potential variation has important consequences on the evolution of galaxies and their chemical enrichment, the dynamics of interstellar gas, and the evolution of individual stellar clusters. In this talk, I will discuss the evolution of the mass function of dense cores (CMF) in a star forming clump, and the transition from the CMF to the IMF. In particular, I will demonstrate how several physical processes such as the coalescence of cores, gas accretion by the cores and feedback by the newly formed OB stars shape the CMF and the corresponding IMF. The influence of different clump and core properties (i.e., their density profiles, their contractions timescales, concentrations, and level of turbulence) in generating variations of the IMF will be highlighted. Finally, I will discuss how the metallicity of the gas in the star forming regions can regulate the star formation rates and efficiency and the implications of this for the galactic star formation laws.