Born at Lyons, Jordan studied in Paris at the Ecole Polytechnique, where he trained as an engineer. Later he taught at both the Ecole Polytechnique and the Collège de France until his retirement in 1912. His interests lay chiefly in pure mathematics, although he made contributions to a wide range of mathematical subjects.

Jordan's most important and enduring work was in group theory and analysis. He was especially interested in groups of permutations and grasped the intimate connection of this subject with questions about the solvability of polynomial equations. This basic insight was one of the fundamental achievements of the seminal work of Evariste Galois, and Jordan was the first mathematician to draw attention to Galois's work, which had until then been almost entirely ignored. Jordan played a major role in starting the systematic investigation of the areas of research opened up by Galois. He also introduced the idea of an infinite group.

Jordan also passed on his interest in group theory to two of his most outstanding pupils, Felix Klein and Sophus Lie, both of whom were to develop the subject in novel and important ways.