This is the only monograph devoted to the expressibility of finitely axiomatizable theories, a classical subject in mathematical logic. The volume summarizes investigations in the field that have led to much of thecurrent progress, treating systematically all positive results concerning expressibility. Also included in this unique text are solutions to both the Vaught-Morely problem and the Hanf problem, and a number of new naturalquestions that provide prospects for further development of the theory.