Jean Leray (1906-1998) was one of the great French mathematicians of his century. His life's work can be divided into 3 major areas, reflected in these three volumes. Volume I, to which an Introduction has been contributed by A. Borel, covers Leray's seminal work in algebraic topology, where he created sheaf theory and discovered the spectral sequences. Volume II, with an introduction by P. Lax, covers fluid mechanics and partial differential equations. 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. Volume III, 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. He was awarded the Malaxa Prize (1938), the Grand Prix in Mathematical Sciences (1940), the Feltrinelli Prize (1971), the Wolf Prizein Mathematics (1979), and the Lomonosov Gold Medal (1988).