A bola amphiphile is composed of two polar head groups attached to the ends of a hydrophobic tail. In this paper, the principles of molecular self-assembly of bola amphiphiles are quantitatively established by applying thermodynamic and geometric considerations developed earlier for the more common one-headed amphiphiles. Bola amphiphiles are found to aggregate into spheres, small spherocylinders, large cylinders, small and large discs and vesicles. Inside these aggregates, the hydrophobic tail is expected to assume both a folded and a fully stretched conformation. In general, the presence of the second polar group in a bola amphiphile causes an increase in the aqueous solubility of the amphiphile, an increase in the cmc and a decrease in the aggregation number when compared to the corresponding one-headed amphiphile. The quantitative principles of self-assembly established here can aid in deciding which bola amphiphiles should be synthesized in order to generate desired organized assemblies.