From the reviews:p}This} book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts of Lie groups and representation theory and outsiders who would like to see connections of some aspects with other parts of mathematics. This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured. -Sergio Console, ZentralblattpThis book is devoted to Harish-Chandras Plancherel inversion formula in the special case of the group SLn(R) and for spherical functions. … the book is easily accessible and essentially self contained. (A. Cap, Monatshefte fr Mathematik, Vol. 140 (2), 2003)pRoughly, this book offers a functorial exposition of the theory of spherical functions developed in the late 1950s by Harish-Chandra, who never used the word functor. More seriously, the authors make a considerable effort to communicate the theory to an outsider. …. However, even an expert will notice several new and pleasing results like the smooth version of the Chevally restriction theorem in Chapter 1. (Tomasz Przebinda, Mathematical Reviews, Issue 2002 j)pThis excellent book is an original presentation of Harish-Chandras general results … . Unlike previous expositions which dealt with general Lie groups, the present book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts … . This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured. Very nice is, for instance, the … table of the decompositions of Lie groups.(Sergio Console, Zentralblatt MATH, Vol. 973, 2001)Harish-ChandraAs general Plancherel inversion theorem admits a much shorter presentation for spherical functions. Previous expositions have dealt with a general, wide class of Lie groups. This has made access to the subject difficult for ou@E”záG® ¾Û€