The alumino-silicate series (Al4+2xSi2-2xO10-x, x = 0-1), is an important class of structural ceramics with many applications. Except for the end member (x = 0), which is the crystalline phase sillimanite, the reported crystal structures of the other phases, called mullites, all have partially occupied sites which makes any theoretical calculation a formidable task. In this article, we describe a systematic and detailed theoretical investigation of the structures and properties of the phases in this series. We constructed stoichiometric supercell models for the four well-known mullite phases 3Al(2)O(3)center dot 2SiO(2), 2Al(2)O(3)center dot SiO2, 4Al(2)O(3)center dot SiO2, 9Al(2)O(3)center dot SiO2, corresponding to x = 0.25, 0.40, 0.67, and 0.842. The construction of the models began with experimentally reported crystal structures followed by systematic removal of selected atoms at the partially occupied sites to maintain charge neutrality. A large number of models were built for each phase and fully relaxed to high accuracy using the Vienna ab initio simulation package program. The model with the lowest total energy for a given x was chosen as the representative structure for that phase. Together with sillimanite (x = 0) and the silica free iota-Al2O3 (x = 1), this series' electronic structure and mechanical properties were studied via first-principles calculations. Their elastic coefficients and mechanical properties (bulk modulus, shear modulus, Young's modulus, and Poisson's ratio) were evaluated. The electronic structure, effective charges, bonding, and optical properties of these mullite phases were calculated using the orthogonalized linear combination of atomic orbitals method. These first-principles results provide the basis for an explanation of the experimentally observed structure and properties of mullite phases and their trends with x at the fundamental level.