<p> One of the most difficult and interesting aspects of the physics of collapse and outflow formation, as well as the evolution of the protostellar disk, is the role of hydromagnetic forces. However, magnetic fields are only coupled to the charged species present in poorly ionized molecular clouds. Ambipolar diffusion-the process by which magnetic fields "slip" in poorly ionized gas-strongly affects the initial cloud as well as the final observable structure through collisional heating. Also, as the gas becomes opaque to cosmic rays, the ionized structure of the accreting gas may become more complex, leading to a neutral 'dead zone' in a layered accretion disk (vital in determining planet masses in planet formation theories (Matsumura & Pudritz, 2005)). We omit possible effects of ionizing radiation in these early stages of formation. </p> <p> In this thesis, we perform fully 3D simulations (using the FLASH AMR code) and have implemented ambipolar diffusion in the MHD module of the code in addition to a broad treatment of cooling (Banerjee et al., 2006). This has allowed us to track the ionized gas and magnetic fields properly from the beginning of collapse down to the onset of outflows. We find that high accretion rates persist on the order 1 of 10-3 M0 yr-(where the core mass has reached about 0.1 M0 ) due to efficient extraction of angular momentum through magnetic processes. Magnetic braking is reduced by about 3/4 in the initial collapse relative to an ideal collapse of same initial conditions. This, with a reduction in magnetic pressure in the disk, leads to an increased rate of fragmentation. One of the major new results of this work is the discovery that outflows from disks still occur even in the presence of ambipolar diffusion. Surprisingly, they are initiated even earlier than outflows from idealized, completely ionized disks. They are generated by a magnetic tower mechanism at central densities of 1012 cm-3, as effective ram pressure on the wound up toroidal field is reduced, allowing it to push away from the disk earlier. </p> <p> We have also shown that the formation of a dead zone in these early stages is dependent on shielding of cosmic rays, in the absence of which a decoupled zone in the disk midplane forms. This region, where the accreting gas is effectively decoupled from the magnetic field, extends 10 AU in radius and (2-3) AU in height from the midplane. The global magnetic field threading such a complex accretion disk shows a dragged out structure, as coupled surface layers of the disk pull in the field. The disk is puffy due to drift heating and the initial stages of the outflow pushing out into the ambient medium. However, overall magnetic field build-up is still efficient, as values of the magnetic field in the disk are only reduced by half. </p> / Thesis / Master of Science (MSc)