The formation of molecular clouds and stars by turbulent compression and collapse The goal of this work is to improve our understanding of the role of interstellar turbulence in star formation. In particular the mechanism of turbulence energy injection the turbulence forcing is investigated with hydrodynamical simulations. In a systematic comparison I study the two limiting cases of turbulence forcing: solenoidal (divergence free) forcing and compressive (curl free) forcing. I show that these two cases yield significantly different gas density and velocity statistics. The fractal structure of the gas and the turbulent density probability distribution function (PDF) are explored in detail. I find that compressive forcing yields a three times higher standard deviation of the roughly Gaussian density PDF. I discuss the impact of this result on analytic models of star formation ...