Topology is the mathematical study of shapes and spaces. It is a major area of mathematics concerned with the most basic properties of space, such as connectedness, continuity and boundary. It is the study of properties that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. 拓撲學（英語：topology）研究的是幾何形體在連續形變，精確地說，雙方一一而且雙方連續的變換（稱為同胚）之下保持不變的性質。理解得廣泛些，拓撲學是研究數學中連續性現象的學科。
| 排名 | 學校 | 學校英文名 | 州/城市 |
|---|
| 1 | 加州大學伯克利分校 | University of California–?Berkeley | Berkeley, CA |
| 2 | 哈佛大學 | Harvard University | Cambridge, MA |
| 3 | 普林斯頓大學 | Princeton University | Princeton, NJ |
| 4 | 麻省理工學院 | Massachusetts Institute of Technology | Cambridge, MA |
| 5 | 斯坦福大學 | Stanford University | Stanford, CA |
| 6 | 芝加哥大學 | University of Chicago | Chicago, IL |
| 7 | 哥倫比亞大學 | Columbia University | New York, NY |
| 8 | 德克薩斯大學奧斯汀分校 | University of Texas–?Austin | Austin, TX |
| 9 | 密歇根大學安娜堡分校 | University of Michigan–?Ann Arbor | Ann Arbor, MI |
| 10 | 康奈爾大學 | Cornell University | Ithaca, NY |
| 11 | 耶魯大學 | Yale University | New Haven, CT |
| 12 | 紐約州立大學石溪分校 | Stony Brook University–?SUNY | Stony Brook, NY |
| 13 | 加州大學戴維斯分校 | University of California–?Davis | Davis, CA |
| 13 | 加州大學洛杉磯分校 | University of California–?Los Angeles | Los Angeles, CA |
| 15 | 布朗大學 | Brown University | Providence, RI |
| 15 | 加州理工學院 | California Institute of Technology | Pasadena, CA |
參考資料：US NEWS Topology Rankings 2013/14 USNEWS排名