For your convenience we list all the lecture notes that you can find on our web site, sorted by the name of the lecturer:

Siegfried Echterhoff

• Crossed products and Morita equivalences
• The Green-Julg theorem
• The Dirac-dual Dirac method and the Baum-Connes conjecture (handwritten by Pierre Clare, thanks!)

Heath Emerson

• Bivariant K-theory for smooth manifolds I
• Bivariant K-theory for smooth manifolds II

The lecture notes were taken by Robin Deeley and Elkaioum Moutuou (thank you!).

Erik Guentner

• Affine Actions and the Baum-Connes conjecture

The lecture notes were taken by Manuel Köhler (Danke!).

Pierre Julg

• K-theory of the C*-algebras of free groups

The lecture notes were taken by Pierre Clare (merci!).

Gennadi Kasparov

• The Dirac-dual Dirac method

The lecture notes were taken by Hang Wang and Dapeng Zhou (many thanks!).

Ralf Meyer

• KK-theory as a triangulated category

The lecture notes were taken by Sigurd Segtnan (cheers!).

Walther Paravicini

Lecture notes for the course Introduction to KK-theory.

• LaTeXed lecture notes (typed by Lin Shan)
• Hilbert modules, adjoinable and compact operators (handwritten)
• Kasparov's stabilisation theorem, tensor products, graded algebras (handwritten)
• Definition of KK-theory, basic properties such as bifunctoriality (handwritten)
• The standard simplifications, the Fredholm picture, KK(\C,B) = K_0(B) (three sketches) (handwritten)
• The Kasparov product: connections, existence (handwritten)
• The Kasparov product: existence continued, a useful lemma (handwritten)
• The Kasparov product: existence (LaTeXed notes for a seminar talk (2004), revised version)
• Overview: The general form of the Kasparov product, long exact sequences
• Bott peridocity of KK-theory (LaTeXed version)
• An informal account of KKban (handwritten notes by Elkaioum Moutuou, thanks!)

Note that the partitioning of the lecture notes does not correspond to individual lectures but rather to natural chapters. Lin Shan has typed most of the lecture notes, so (most of) the handwritten notes are redundant. Thank you, Lin!

As I did not cover the construction of the homotopy between gamma and 1 in KKban in my talk on KKban I would like to draw your attention to the lecture notes by Georges Skandalis of the fourth in a series of four talks on KK-theory given in the course of the Sixth Anual Spring Institute on Noncommutative Geometry And Operator Algebras 2008 at Vanderbilt University, Nashville.

Georges Skandalis

These are the notes for the first and the fourth lecture of the lecture series on Index theory and KK-theory given by Ryszard Nest and Georges Skandalis. The lecture notes were taken by Hang Wang and Dapeng Zhou.

• Index theory and KK-theory (lectures 1 and 4)