Can anyone suggest me some good books where I can find integration theory on semisimple Lie groups (using KAK, KAN and other type of decompositions)?

I have read Knapp's book "Lie groups beyond introduction". He discusses integration formula for Iwasawa decomposition. I want to know all the integration formulas for semisimple Lie group, and I need a book built up from very basic theory of Lie groups and Lie algebras.

Helgason's book "Groups, geometry and Analysis " has this. But I want some book where things start from more basic treatments. It seems to me that in order to read "Groups, geometry and Analysis" I need to read Helgason's first book also. Till now I am quite comfortable with Lie group and Lie algebra theory as Knapp treats it, which do not require any Riemannian geometry.

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    $\begingroup$ Maybe you have no choice but to look through Helgason's book "Differential Geometry, Lie Groups, and Symmetric Spaces". I think you can read about the structure of semisimple groups and skip Riemannian geometry, if you don't want to learn it now. $\endgroup$ Jun 17, 2020 at 16:57


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