The formation and evolution of the circumstellar disc in the collapsing molecular cloud with and without magnetic field is investigated from the pre-stellar stage resolving both the molecular cloud core and the protostar itself. In the collapsing cloud core, the first (adiabatic) core appears prior to the protostar formation. Reflecting the thermodynamics of the collapsing gas, the first core is much more massive than the protostar. When the molecular cloud has no angular momentum, the first core falls on to the protostar and disappears a few years after the protostar formation. On the other hand, when the molecular cloud has an angular momentum, the first core does not disappear even after the protostar formation, and directly evolves into the circumstellar disc with a Keplerian rotation. There are two paths for the formation of the circumstellar disc. When the initial cloud has a considerably small rotational energy, two nested discs appear just after the protostar formation. During the early main accretion phase, the inner disc increases its size and merges with the outer disc (i.e. first core) to form a single circumstellar disc with a Keplerian rotation. On the other hand, when the molecular cloud has a rotational energy comparable to observations, a single centrifugally supported disc that corresponds to the first core already exists prior to the protostar formation. In such a cloud, the first core density gradually increases, maintaining the Keplerian rotation and forms the protostar inside it. The magnetic field rarely affects the early formation of the circumstellar disc because the magnetic field dissipates in the high-density gas region where the circumstellar disc forms. As a result, in any case, the protostar at its formation is already surrounded by a massive circumstellar disc. The circumstellar disc is about 10-100 times more massive than the protostar in the main accretion phase. Such discs are favourable sites for the formation of binary companions and gas-giant planets.
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