结构数学是20世纪数学发展的一条主线，其显著特点是集合论基础之上的抽象化、公理化和结构化。本项目针对20世纪结构数学的特点从结构数学的基本概念、相关理论、交叉应用及关键人物四个方面进行研究。深入挖掘和筛选有价值的结构数学史料，特别是数学家的一手资料、原始文献；用思想史学派的概念分析法研究微分流形、李群李代数、纤维丛、典型群、组合群等基本概念的起源发展；探讨和总结在这些基本概念基础上形成的微分流形理论、李理论、纤维丛和示性类理论、无限群理论的研究方法、手段、路线；考察学科的交叉应用，以李理论、表示论、纤维丛理论间的交叉应用为典型代表对代数拓扑、微分拓扑、代数几何、微分几何、调和分析等学科间的交叉应用进行研究；对结构数学有重要贡献的数学家树碑立传，如塞尔伯格、盖尔范德、哈瑞什-钱德拉、惠特尼等。对结构数学在20世纪发展的研究，可深化知识间的联系,强化学科间交叉,为理解和把握数学提供有益的借鉴。

Structural mathematics is the main thread of the development of the mathematics in 20th century,characterized by the abstraction,the axiomatization and the structuring basing on the set theory. Upon its characteristics, the project is aiming at four aspects:fundamental concepts,relative theories, intersections and applications,key mathematcians.Excavating and selecting valuable historical materials,especially the original literatures and primary sources; researching the evolution of the fundamental concepts- - differential manifolds,lie groups and lie algebras,fiber bundles,classical groups and combinational groups- - by the conceptual analysis of school of the thought history; discussing and summarizing the methods,approaches and outlines of the theory basing on the fundamental concepts;investigating the interactions and the applications among these subjects:algebraic topology,differential topology,algebraic geometry,differential geometry,harmonic analysis,especially the Lie theory,representation theory and the fiber bundle theory;writing biographies of important mathematicians for structural mathematics, for instance,A.Selberg,I.Gelfand,Harish-Chandra,H.Whitney. All these researches will deepen the association between mathematical knowledge, similarly strengthen the interdisciplinary. As well as, it can offer the reference to understanding and comprehending mathematics.