Marius Sophus Lie (1842–1899) was a pioneer of study of (and almost solely devoted to) the groups of continuous and smooth transformations, mainly motivated by symmetries of differential equations. He is the founder of the theory of Lie groups and Lie algebras, whose global theory however has been completed only with works of Élie Cartan.
On “transformation groups”, that would come to be called Lie groups:
Sophus Lie: Theorie der Transformationsgruppen I, Math. Ann. 16 (1880) 441–528 [doi:10.1007/BF01446218]
Sophus Lie unter Mitwirkung von Friedrich Engel: Theorie der Transformationsgruppen, Teubner (1888) [ark:/13960/t25b0068w]
English translation:
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