A methodical analysis of the research related to the article, ``Sur les groupes continus'', of Henri Poincar\'{ e} reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the precedence of his discovery of many important concepts, especially that of the \textit{ universal enveloping algebra} of a Lie algebra over a field of characteristic zero, the \textit{ % canonical map} (\textit{ symmetrization}) of the symmetric algebra onto the universal enveloping algebra. The essential part of this article consists of a detailed discussion of his rigorous, complete, and enlightening proof of the so-called Birkhoff-Witt theorem.
Categories: math.HO