This volume contains the lectures given during the colloquium held in Lyon in 1989 and devoted to the memory of Edmond Combet. The subjects discussed during this meeting are those that Edmond Combet liked, and lie at the intersection of analysis, geometry and mathematical physics. The papers presented contain evocations of Combet's mathematical works by A. Lichnerowicz and by J.-P. Bourguignon, and articles from P. Bérard, J.-M. Bismut, Y. Choquet-Bruhat, Y. Colin de Verdière, J.-P. Françoise, E. Ghys and J.-C. Sikorav.