中文摘要：

流形概念是20世纪数学的最具代表性的基本观念之一。文章分析与探讨流形概念的起源与发展。特别地，研究了流形概念从产生到其概念的精确的数学描述这一历史过程。

英文摘要：

The concept of manifold is one of the most representative mathematical basic idea in the 20th century. The origin and the development of the concept of manifold are analyzed and discussed. Specially,a historical survey of the concept of manifold from the origin to its accurate mathematical representation is given.