The Erlangen program (in German, erlanger Programm) is a project, begun by Felix Klein at Erlangen in the 19th century, to study geometry from the perspective of group theory. It was published in 1872 as Vergleichende Betrachtungen über neuere geometrische Forschungen, translated by M. W. Haskell as A Comparative Review of Recent Researches in Geometry. We now use groupoids and even categories or -groupoids.
See John Baez’s webpage.