Friedrich Schur studied differential geometry, transformation groups (Lie groups) after Sophus Lie. Many of his results, which he summarized in his book Grundlagen der Geometrie (Foundation of Geometry) of 1909, can also be found in the work of David Hilbert without reference to Schur. He also wrote a textbook of analytical geometry (1898) and the graphical statics (1915).
In 1912, he received the Lobachevsky Prize for his book Grundlagen der Geometrie, a Russian prize. In 1910, he was chairman of the German Mathematical Society. He holds honorary doctorates from the University of Karlsruhe. In 1927, he was selected as a corresponding member of the Bavarian Academy of Sciences.
Among his students was Theodor Molien and Julius Wellstein.