This book provides a comprehensive treatment of multilinear operator integral techniques. The
exposition is structured to be suitable for a course on methods and applications of multilinear
operator integrals and also as a research aid. The ideas and contributions to the field are
surveyed and up-to-date results and methods are presented. Most practical constructions of
multiple operator integrals are included along with fundamental technical results and major
applications to smoothness properties of operator functions (Lipschitz and Hölder continuity
differentiability) approximation of operator functions spectral shift functions spectral
flow in the setting of noncommutative geometry quantum differentiability and
differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases
while more involved technical proofs are outlined and supplemented with references. Selected
open problems in the field are also presented.
