Henri Poincaré was the first to introduce four-vectors, the Lorentz group and its invariants (including the space-time metric), “Poincaré stresses,” as well as making other valuable contributions to relativity theory. We owe to him the names: “Principle of Relativity,” “Lorentz group,” “Lorentz transformation,” and “invariants of the Lorentz group.” It will be shown that his main contributions to relativity were those of a mathematical nature. This has not been sufficiently recognized, although his physical contributions to relativity have been much discussed recently. Frequent misunderstanding of the work of Poincaré and Einstein has resulted in controversy tending to obscure the main achievements of Poincaré. The Poincaré stresses are discussed because of widespread ignorance regarding the theory of classical fundamental charges. The emphasis in this article is on those accomplishments of Poincaré by which he should be better known today. In addition, some misconceptions about the history of relativity and classical electron theory will be corrected.