  We give a simple unified theory of vortex nucleation and vortex lattice
formation which is valid from the initiation process up to the final
stabilization of the lattice. We treat the growth of vortex lattices from a
rotating thermal cloud, and their production using a rotating trap. We find
results consistent with previous work on the critical velocity or critical
angular velocity for vortex formation, and predict the initial number of
vortices expected before their self assembly into a lattice. We show that the
thermal cloud plays a crucial role in the process of vortex lattice nucleation.

Condensed Matter