Felix Hausdorff graduated from Leipzig in 1891, and then taught there until 1910 when he went to Bonn. Within a year of his appointment to Leipzig he was offered a post at Göttingen but he turned it down.

Hausdorff's main work was in topology and set theory. He introduced the concept of a partially ordered set, and from 1906 to 1909 he proved a series of results on ordered sets. In 1907, he introduced special types of ordinals in an attempt to prove Cantor's continuum hypothesis. He also posed a generalization of the continuum hypothesis. Hausdorff proved further results on the cardinality of Borel sets in 1916.

Building on work by Fréchet and others, he created a theory of topological and metric spaces. Earlier results on topology fitted naturally into the framework set up by Hausdorff. In 1919, he introduced the notion of Hausdorff dimension, sometimes called fractal dimension. He also introduced the Hausdorff measure and the term "metric space" is due to him.

Hausdorff worked at Bonn until 1935 when he was forced to retire by the Nazi regime. Although as early as 1932 he sensed the oncoming calamity of Nazism, he made no attempt to emigrate while it was still possible. As a Jew his position became more and more difficult. In 1941 he was scheduled to go to an internment camp but managed to avoid being sent. However by 1942 he could no longer avoid being sent to the internment camp and, together with his wife and his wife's sister, he committed suicide.