These lectures attempt to expose the most important ideas, which have been proposed to explain the formation of stars with particular emphasis on the formation of brown dwarfs and low-mass stars. We first describe the important physical processes which trigger the collapse of a self-gravitating piece of fluid and regulate the star formation rate in molecular clouds. Then we review the various theories which have been proposed along the years to explain the origin of the stellar initial mass function paying particular attention to four models, namely the competitive accretion and the theories based respectively on stopped accretion, MHD shocks and turbulent dispersion. As it is yet unsettled whether the brown dwarfs form as low-mass stars, we present the theory of brown dwarfs based on disk fragmentation stressing all the uncertainties due to the radiative feedback and magnetic field. Finally, we describe the results of large scale simulations performed to explain the collapse and fragmentation of molecular clouds.