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 Prize in Mathematics (1979), and the Lomonosov Gold
Medal (1988).