A central problem in the theory of star formation is to understand the spectrum of masses, or Initial Mass Function, with which stars are formed. The fundamental role of the IMF in galactic evolution has been described by Tinsley (1980), and an extensive review of evidence concerning the IMF and its possible variability has been presented by Scalo (1986). Although the IMF derived from the observations is subject to many uncertainties, two basic features seem reasonably well established. One is that the typical stellar mass, defined such that equal amounts of matter condense into stars above and below this mass, is within a factor of 3 of one solar mass. A theory of star formation should therefore be able to explain why most stars are formed with masses of order one solar mass. The second apparently universal feature is that the IMF for relatively massive stars can be approximated by a power law with a slope not greatly different from that originally proposed by Salpeter (1955). Thus we also need to understand why the IMF always has a similar power-law tail toward higher masses.