Abstract
This paper provides a detailed study of the historical development of the theory of infinite continuous groups from its dawn in 1883 up to the publication of Jules Drach's thesis in 1898. The aim is twofold. First, to describe the emergence of the notion in Lie's works and to treat the classification problem of all infinite continuous groups. Second, to emphasize the great importance which infinite continuous groups played in the historical development of integration theory of partial differential equations.
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