  Fifty years after Ed Salpeter's seminal paper, tremendous progress both on
the observational and theoretical sides allow a fairly accurate determination
of the Galactic IMF not only down to the hydrogen-burning limit but into the
brown dwarf domain. The present review includes the most recent observations of
low-mass stars and brown dwarfs to determine this IMF and the related Galactic
mass budget. The IMF definitely exhibits a similar behaviour in various
environments, disk, young and globular clusters, spheroid. Small scale
dissipation of large scale compressible MHD turbulence seems to be the
underlying triggering mechanism for star formation. Modern simulations of
compressible MHD turbulence yield an IMF consistent with the one derived from
observations.
