Jean Leray is one of the great French mathematicians of this century. His life's work divides into 3 major areas, reflected in these 3 volumes. Vol. 1, to which an Introduction in English has been contributed by A. Borel, covers Leray's seminal work in algebraic topology, where he created sheaf theory and discovered the spectral sequences. Vol. 2, with an introduction by P. Lax, covers fluid mechanics and PDE: Leray demonstrated the existence of the infinite-time extension of weak solutions of the Navier-Stokes equations; 60 years later this profound work has retained all its impact. Vol. 3, on the theory of several complex variables, has a long introduction by G. Henkin. Leray's work on the ramified Cauchy problem will stand for centuries alongside the Cauchy-Kovalevska theorem for the unramified case.