This is an interdisciplinary course covering the fundamental laws of the mechanics and physics of crystalline solids, the general description of a periodic structure and their specific characterization methods. The course will start with tensor analysis, and basic calculations of tensor fields. After that, basic kinematics such as deformation gradient, Cauchy-Green tensor will be introduced and defined, followed by the mathematical description of symmetry of crystals. Finally, the course will discuss reciprocal lattices and the X-ray diffraction for structural solving.