本书是F.克莱因的名著，其内容是作者在临终前一两年给部分同事所作的讲演，而由他的学生们编辑成书。书中介绍了数学科学在19世纪的发展。在本卷(第一卷)中， 克莱因非常详尽而且有批判性地分析了高斯、黎曼、魏尔斯特拉斯、柯西、伽罗瓦等一大批最重要的数学家的数学思想和贡献；同时也介绍了一大批物理学(特别是数学物理学)大师如开尔文、麦克斯韦、亥姆霍兹的思想和业绩；并详细讨论了一些最重要的数学分支（函数论、射影几何、代数几何等）的缘起和前景。
本书适合从事数学的研究和教学的大学水平以上的学生和教师学习参考，也适合研究科学史、数学史和关心、研究一般的科学思想文化发展的读者阅读。
- 前辅文
- Introduction
- Chapter I Gauss
- Applied Mathematics
- Pure Mathematics
- Chapter II France and the Ecole Polytechnique in the First Decades of
- the Nineteenth Century
- Mechanics and Mathematical Physics
- Geometry
- Analysis and Algebra
- Chapter III The Founding of Crelle’s Journal and the Rise of Pure
- Mathematics in Germany
- The Analysts of Crelle’s Journal
- The Geometers of Crelle’s Journal
- Chapter IV The Development of Algebraic Geometry After Moebius,
- Pluecker and Steiner
- The Elaboration of a Purely Projective Geometry
- The Parallel Development of Algebra: Invariant Theory
- N-dimensional Space and General Complex Numbers
- Chapter V Mechanics and Mathematical Physics in Germany and
- England Until About 1880
- Mechanics
- Mathematical Physics
- Chapter VI The General Theory of Functions of Complex Variables
- According to Riemann andWeierstrass
- Bernhard Riemann
- Karl Weierstrass
- Chapter VII Deeper Insight into the Nature of Algebraic Varieties and
- Structures
- The Further Development of Algebraic Geometry
- The Theory of Algebraic Integers and Its Interaction with the Theory of
- Algebraic Functions
- Chapter VIII Group Theory and Function Theory
- Functions
- Group Theory
- Automorphic Functions
