  Collapse of the rotating magnetized molecular cloud core is studied with the
axisymmetric magnetohydrodynamical (MHD) simulations. Due to the change of the
equation of state of the interstellar gas, the molecular cloud cores experience
several different phases as collapse proce eds. In the isothermal run-away
collapse ($n \lesssim 10^{10}{\rm H_2 cm}^{-3}$), a pseudo-disk is formed and
it continues to contract till the opaque core is fo rmed at the center. In this
disk, a number of MHD fast and slow shock pairs appear running parallelly to
the disk. After the equation of state becomes hard, an adiabatic core is
formed, which is separated from the isothermal contracting pseudo-disk by the
accretion shock front facing radially outwards. By the effect of the magnetic
tension, the angular momentum is transferred from the disk mid-plane to the
surface. The gas with excess angular momentum near the surface is finally
ejected, which explains the molecular bipolar outflow. Two types of outflows
are observed. When the poloidal magnetic field is strong (magnetic energy is
comparable to the thermal one), a U-shaped outflow is formed in which fast
moving gas is confined to the wall whose shape looks like a capit al letter U.
The other is the turbulent outflow in which magnetic field lines and velocity
fi elds are randomly oriented. In this case, turbulent gas moves out almost
perpendicularly from the disk. The continuous mass accretion leads to the
quasistatic contraction of the first core. A second collapse due to
dissociation of H$_2$ in the first core follows. Finally another quasistatic
core is again formed by atomic hydrogen (the second core). It is found that
another outflow is ejected around the second atomic core, which seems to
correspond to the optical jets or the fast neutral winds.
