The two competing theories of star formation are based on turbulence and ambipoar diffusion. I will first briefly explain the two theories. There have been analytical (or semi-analytic) models, which estimate star formation rates in a turbulent cloud. Most of them are based on the log-normal density PDF (probability density function) of the turbulent cloud without self-gravity. I will first show that the core (star) formation rate can be increased significantly once self-gravity of a turbulence cloud is taken into account. I will then present the evolution of molecular line profiles of HCO+ and C18O toward a dense core that is forming inside a magnetized turbulent molecular cloud. Features of the profiles can be affected more significantly by coupled velocity and abundance structures in the outer region than those in the inner dense part of the core. During the evolution of the core, the asymmetry of line profiles easily changes from blue to red, and vice versa. Finally, I will introduce a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamic code.