公元前4世纪，欧几里得《几何原本》树立了公理系统之典范，成为了传世之作。19世纪末， 在希尔伯特笔下，另一部公理领域的著作《几何基础》问世了。它承袭《几何原本》之风格，完善了公理系统，加固了几何之根基。那么，希尔伯特的公理系统是如何形成的？他曾受到哪些因素的影响？现在流形的版本与早期版本有何区别？这套公理系统又在后来产生了多大的影响？希尔伯特《几何基础》一经出版后便很快在高校中普及,20世纪中国出现了多种版本的几何基础教材，这些教材与希尔伯特《几何基础》有多大关系？本文分为四个部分：第一章，回顾从《几何原本》到《几何基础》之间的历史。第二章，介绍了在数学或物理学方面对希尔伯特公理产生影响的学者，包括帕士、赫兹等人；理清了从1891年开始到1899年公理系统形成的过程；对比了关键的第七版与第一版的差异。第三章，20世纪中国的几何基础教材可以划分为两个阶段，二、三十年代及中后期，前一时期以陈藎民和傅种孙为代表，主要受欧美影响；后一时期以陆钦轼、钱端壮和傅章秀为代表，主要受前苏联影响。笔者通过对这些教材间公理系统的比较，明确了它们的继承关系。第四章，前一章所述经典教材已成为历史，国内几何基础课程逐渐被冷落；笔者搜索了美国33所院校，仍有这门课程；于是从数学教育的角度，分析这门课的价值，最后建议保留几何基础课程。

In the 4th century B.C,Euclid’s Elements set an example of axiom system, and became masterpieces. At the end of the 19th century, another book about axiom came out by Hilbert. It inherited the style of the Elements, improved the axiom system, and reinforced the foundations of geometry. Then how had Hilbert’s axiom system formed? What he was affected by? What’s the difference between the manifold version now and the earlier version? And how much impact it produced later? When Hilbert’s Foundations of Geometry had been published, it became popular in colleges soon. In the 20th century, several versions of teaching material about the foundations of geometry appeared in China. How these teaching materials evolved from the Foundations of Geometry?This article is divided into four parts:First, I review the history from the Euclid’s elements to Hilbert’s Foundations of Geometry.Second, I introduce the scholars who in mathematics or physics that impact on Hilbert’s axioms; and clarified the process of the axioms forming from 1891 to 1899; and then compared the difference of the seventh edition and the first edition of Hilbert’s Foundations of Geometry.Third, the teaching materials of Foundations of Geometry in the 20th century in China can be divided into two phases, in two、thirty time and after. Chen Jin Min and Fu Zhong Sun were the representative of the previous period, mainly influenced by European and American; Lu Qin Shi、Qian、Duan Zhuang and Fu Zhang Xiu were the representative of the latter period, mainly influenced by the former Soviet. I clarified the inheritance relationship of these materials through compared their axiom system.Fourth, the classic textbook described in the previous chapter has become the past, the course of Foundations of Geometry was neglected gradually. I searched 33 colleges in America, and found that the course is still. So I based on the perspective of mathematics education, analysis the value of this course, and suggest that we can teach the Foundations of Geometry in the course of Higher Geometry.