拓扑学始于19世纪，是由欧拉、黎曼、庞加莱等发展起来的一个重要的几何分支。现在它已成为研究连续性现象的重要工具，其基本内容已经成为现代数学的常识。本课程将阐述拓扑学的概念和方法在自然科学、人文科学，还有日常生活中的作用，涉及到数学中的其他分支（如几何和群论等）、经济学和博弈论等。
Topology theory was developed by Euler, Riemann, Poincare etc. , which is now a fundamental subject concerning about the continuity. By a series of lectures, we will introduce basic concept and methodology in topology as well as their applications in the other branches of mathematics and science.