A detailed investigation is presented of the theory of phase transitions afforded by the random phase approximation (RPA) and Gaussian fluctuation theory. Arguments are given which indicate that these two theories are equivalent. A rigorous analysis is carried out on the RPA for a simple binary model that should exhibit a phase transition. It is found that when the RPA free energy is used to calculate the thermodynamics for the model a catastrophe region exists in which the system collapses to negatively infinite free energy and thermodynamic stability breaks down before (at lower densities and higher temperature) the region is reached. The catastrophe surface which surrounds the region has been identified in the previous literature as the limit of stability for the model, and the singularities associated with the catastrophe have been incorrectly identified as true critical singularities. The incorrect identification leads to results which contradict the second law of thermodynamics. It is shown that there is no sensible solution to the equations obtained from a Maxwell construction to bridge the catastrophe. The RPA for the binary model is also discussed within the context of the compressibility theorem. When this route to the thermodynamics is taken, it is found that the behavior predicted by the RPA is purely classical. Arguments are presented which indicate that the results found with the binary model are general features of the RPA; the application of the approximation to more general one- and two-component systems yield the same results. Finally, a tentative explanation for the catastrophe is given. The explanation suggests a modified RPA which does not violate the second law of thermodynamics; however, the patched up theory is classical.