Reference request for Plancherel measure I need a good reference for the basic definitions of the dual of locally compact group (not necessarily abelian), its natural topology, $\sigma$-algebra, and the Plancherel measure on it (when they are defined). This topic seems pretty standard to me, but when I needed a basic reference on this (both to check my memories and to be able to cite it in a paper I am writing), I didn't find one. 
By the way, the wikipedia webpage "Plancherel measure" should be completely rewritten. 
There is not even  a definition, just a list of examples (and the definition given in the finite case is not compatible with the one given in the compact case). I would be happy to rewrite it, when I have a reference to check the details.  
 A: Hartmut Fuehr's book (Abstract harmonic analysis of continuous wavelet transforms,
 Springer Lecture Notes in Mathematics, Nr. 1863, 2005, X, 193 p., Softcover
ISBN: 3-540-24259-7), contains a "-reasonably self-contained- exposition of Plancherel theory", see also http://www.matha.rwth-aachen.de/~fuehr/book.html.
Then there is also Dixmier's book: J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, 1969.
A: In my humble opinion the best reference is Dixmier $C^*$-algebras. The first half of the book has a very complete explanation of what you need to know about $C^*$-algebras. In chapter 8 he goes over what is the decomposition of a trace for $C^*$-algebras. Then from Chapter 13 on he goes into the theory for a locally compact group. He explains necessary and sufficient conditions for the Plancherel formula to exist (has to be Type I, separable, postliminal, unimodular etc.). He also explains the topology to be given $\widehat{G}$; in fact he gives three different topologies on this set, and shows all of them agree in the case we are interested in—it is just that beautiful of a book. Chapter 18 is the statement of the Plancherel Theorem; the proof essentially is the one in Chapter 8 for $C^*$-algebras. The english version is very good, with very few typos or print mistakes that may confuse you. I have not found a typo or a mistake of any sort in the French version. I think it is a very good book, like reading a novel. 
