  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.
