Friedrich Hirzebruch (1927-2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure of his generation, both scientifically and for his role in rebuilding German and European mathematics after the war. Hirzebruch's first great mathematical achievement was the proof, in 1954, of the generalization of the classical Riemann-Roch theorem to higher-dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem and the Atiyah-Singer index theorem. He received many awards and honors, including the Wolf prize in 1988, the Lobachevsky prize in 1990, and fifteen honorary doctorates.