A new kind of cell theory-one which formally accounts for the possibility of amorphous phases-is presented. The equilibrium partition function is transformed exactly by first classifying all particle configurations according to multidimensional potential-energy minima and then assigning to each minimum a system-spanning set of cells such that, for configurations near enough the minimum, each cell contains one particle. The theory is then extended to general amorphous systems, and approximate descriptions of supercooled liquids and glass transitions are given.