His PhD thesis, defended in 1952 under the supervision of Joseph Pérès and André Lichnerowicz, was entitled "Sur la stabilité des avions" (On the stability of planes).

[4] Between 1952 and 1958 he worked at Institut des Hautes Études in Tunis, and since 1958 he was Professor of Mathematics at the University of Provence in Marseille.

[5] Souriau contributed to the introduction and the development of many important concepts in symplectic geometry, arising from classical and quantum mechanics.

[6] In particular, he introduced the notion of moment map,[7][8] gave a classification of the homogeneous symplectic manifolds (now known as the Kirillov–Kostant–Souriau theorem), and investigated the coadjoint action of a Lie group, which led to the first geometric interpretation of spin at a classical level.

[11][12] Souriau published more than 50 papers in peer-review scientific journals,[13] as well as three monographs, on linear algebra,[14] on relativity[15] and on geometric mechanics.