This is an expository article on modern crystallography based on discrete geometric analysis, a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability, which has been developed in the last decade. The mathematical part relying on algebraic topology is fairly elementary, but may be still worthwhile for crystallographers who want to learn how well-established mathematics is effectively used in the practical science. A brief history of crystallography is also explained.

中文翻译：

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拓扑晶体学讲座

这是一篇基于离散几何分析的现代晶体学的说明性文章，它是过去几十年发展起来的几种传统学科的混合领域：图论，几何学，离散群论和概率论。依赖于代数拓扑的数学部分是相当基本的，但对于想要学习如何在实践科学中有效使用成熟的数学的晶体学家来说，仍然值得。还解释了晶体学的简要历史。