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The need for comparison methods between crystal structures led the research to look for proper descriptors that could encode the chemical properties of different materials. Many crystal structures exist in theory, but only some of them may be synthesized in a laboratory and used in the real world for practical applications. To discover new materials, Crystal Structure Prediction is vital in predicting various crystal structure forms or generating new ones by building blocks or molecules. Usually, a structure prediction computes chemical features that are not correct properties because they do not consider the entire 3-dimensional structure of a crystal. However, they rely on rules considering only the type of particles involved. For example, some chemical properties are used frequently to select a good candidate for synthesis because, in theory, they could tell if a crystal may exist in its solid form under some environmental conditions. This thesis project aims to design and develop new geometric tools or properties that can properly distinguish 3-dimensional structures starting from the raw atom coordinates. The Geometric features developed in this document are fast properties or numerical characteristics that map crystal structure to a different space for a more reliable and efficient comparison. Firstly, we solved the comparison problem between crystal lattices by designing a property that maps a crystal lattice to the space of polyhedra and a metric that can distinguish them. Secondly, we designed a new and faster geometric property that relies on vectors of interatomic distances that are proved to change continuously under atom perturbations. Finally, the chemical property prediction was addressed in our last work, where we attempted to predict the chemical properties of crystals by using our geometric features.