We present in this paper a statistical model of the growth of amorphous and crystalline structures which is applied here for the investigation of binary glasses. Having defined local configurations (referred to as singlets in what follows), and the ways in which they can assemble together, we establish the statistics of doublets and triplets produced by agglomeration. We obtain fairly good predictions for the glass transition temperature , the composition of mixtures of glass and crystalline phases at x = 0.5, and the and phases for greater values of x. The model predicts also the ratios of typical microstructures and other interesting data, among which are the cooling rates that are necessary to form the glass.