The Earliest Stages of Star and Planet Formation: Core Collapse, and the Formation of Disks and Outflows

(Abridged) In this review we focus on the observations and theory of the formation of early disks and outflows, and their connections with the first phases of planet formation. Large rotationally supported circumstellar disks, although common around more evolved young stellar objects, are rarely detected during the earliest, "Class 0" phase; however, a few excellent candidates have been discovered recently around both low and high mass protostars. In this early phase, prominent outflows are ubiquitously observed; they are expected to be associated with at least small magnetized disks. Disk formation - once thought to be a simple consequence of the conservation of angular momentum during hydrodynamic core collapse - is far more subtle in magnetized gas. In this case, the rotation can be strongly magnetically braked. Indeed, both analytic arguments and numerical simulations have shown that disk formation is suppressed in the strict ideal magnetohydrodynamic (MHD) limit for the observed level of core magnetization. We review what is known about this "magnetic braking catastrophe", possible ways to resolve it, and the current status of early disk observations. Outflows are also intimately linked to disk formation; they are a natural product of magnetic fields and rotation and are important signposts of star formation. We review new developments on early outflow generation since PPV. The properties of early disks and outflows are a key component of planet formation in its early stages and we review these major connections.