| This thesis explores the mechanical and superconducting properties of materials using ab initio calculations. First, calculations of the ideal strength are presented, beginning with calculations of the ideal shear strength of aluminum and copper, which are both ductile fcc metals. The ideal shear strength of tungsten is then investigated. Tungsten has the interesting property that dislocations are active on several slip systems. A study of the ideal shear and tensile strength of molybdenum and niobium is then presented, which provides an interesting comparison in that the shear strength of niobium is suprisingly low, which leads to a different failure mode in the two systems. Calculations of the ideal shear and tensile strength of diamond, silicon and germanium are then presented. These are very different materials from those listed above since they are covalently bonded insulators and semiconductors. A study of BC2N is then presented, which is a recently synthesized and very hard material which has a structure similar to that of diamond. The next study reported concerns polonium, which is unusual in that it is the only element that takes the simple cubic structure. The properties of the recently discovered superconductor MgB2 are then studied theoretically. First, a summary of its electronic structure and phonon properties is presented, followed by a description of the results of an anisotropic Eliashberg calculation of its superconducting properties. Finally, calculations of the electronic properties and ideal strength of MoSe nanowires are presented. |