  We present a new model of homogeneous aggregation that contains the essential
physical ideas of the classical predecessors, the Becker-Doring and
Lifshitz-Slyovoz models. These classical models, which give different
predictions, are asymptotic limits of the new model at small and large cluster
sizes (respectively). Since the new theory is valid for large and small
clusters, it allows for a complete description of the nucleation process;
predicting the Zeldovich nucleation rate, and the diffusion limited growth of
large clusters. By retaining the physically valid ingredients from both models,
we can explain the seeming incompatibilities and arbitrary choices of the
classical models.
  We solve the equations of our new model asymptotically in the small
super-saturation limit. The solution exhibits three successive `eras':
nucleation, growth, and coarsening, each with its specific scales of time and
cluster size. During the nucleation era, the bulk of the clusters are formed by
favorable fluctuations over a free energy barrier, according to the analysis by
Zeldovich. During the Growth era no new clusters are created, and the expansion
of the existing ones continues. Eventually the coarsening era begins. During
this competitive attrition process, smaller clusters dissolve and fuel the
further growth of the larger survivors. By resolving the preceding creation and
growth eras, our analysis gives explicitly the characteristic time and cluster
size of the coarsening era, and a unique selection of the long time,
self-similar cluster size distribution.
