In Chaps. 7 – 9 , we established that the diffraction pattern of a single crystal or a polycrystalline material is transformation of an ordered atomic structure into reciprocal space rather than a direct image of the structure itself. The three-dimensional arrangement of atoms in a lattice can be reconstructed only after the diffraction pattern has been transformed back into direct space. However, in powder diffraction, the situation is complicated by the fact that the diffraction pattern is a one-dimensional projection of three-dimensional reciprocal space. We have no intention of covering the comprehensive derivation of the relevant mathematical tools since it is mainly of interest to experts and can be found in many excellent books and reviews. Therefore, in this chapter, we only briefly describe a general approach to solving the crystal structure, covering the phase problem—a main obstacle in structure determination—the Fourier transformation—a quintessential tool for completing the structure determination—and related topics.