  '
  The theory of KMS weights is based on a theorem of Combes and a theorem of
Kustermans. In applications to KMS states for flows on a unital $C^*$-algebra
the relation to KMS weights of the stabilized algebra has proved useful and
this relation hinges on a theorem of Laca and Neshveyev. The first three
chapters present proofs of these fundamental results that require a minimum of
prerequisites; in particular, they do not depend on the modular theory of von
Neumann algebras. In contrast, starting with chapter four the presented
material draws heavily on the modular theory of von Neumann algebras. Most
results are known from the work of N. V. Pedersen, J. Quaegebeur, J. Verding,
J. Kustermans, S. Vaes, A. Kishimoto, A. Kumjian and J. Christensen, but new
ones begin to surface. In chapter nine and the Appendices D and E the reader
can find a presentation of results obtained recently by the author, partly in
collaboration with G. A. Elliott and Y. Sato. This material is a natural
culmination of methods developed around 1980 by Bratteli, Elliott, Herman and
Kishimoto. Finally, in chapter ten there is a short presentation of the notion
of factor types for KMS weights and states.
