Self-assembled monolayers of amphiphilic surfactant molecules form spontaneously on solid surfaces by exposure to dilute solutions of the adsorbate molecules. We report observations of the growth and desorption/dissolution processes for monolayers of octadecylphosphonic acid (OPA, CH3(CH2)(17)PO(OH)(2)) on mica. We find that these monolayers form via a mechanism that includes nucleation, growth, coalescence, etc, of densely-packed submonolayer islands of the long-chain organic molecules. In situ AFM measurements allow a quantitative analysis of island nucleation and growth rates as well as determination of the island size distribution as a function of coverage. In the growth regime, the nucleation and growth rates have a power law behavior consistent with a simple point island model of 2D cluster growth. In the aggregation regime, the island size distributions are shown to scale with a single evolving length scale in accordance with the dynamical scaling approximation. The desorption/dissolution process proceeds by nucleation of holes in the monolayer that grow and percolate across the sample, leaving isolated islands that gradually decrease in size. The relative rates of hole growth and hole nucleation suggest that removing a molecule from the monolayer/hole boundary is about 5 x 10(4) times more likely than removing a molecule from within a continuous region of monolayer. The coverage kinetics during dissolution can be quantitatively described by a model that incorporates desorption from; "hole" regions and diffusive solution-phase transport through a stagnant layer of finite thickness that can be altered by solvent flow or stirring. If the monolayer is brought into contact with a small enough volume of stagnant solvent, the surface coverage eventually stabilizes due to the buildup of adsorbate molecules in solution. Under these conditions of steady-state surface coverage, the local dynamical processes of island shrinkage, growth, and nucleation continue, eventually leading to a distinctive (decaying exponential) island size distribution characteristic of the system.