My question is about the correct order to read the papers by Arthur on trace formula. Arthur's papers are perfectly well-written, but maybe a little too hard for me to go through easily.


I would like to start with unrefined trace formula, but there are bunches of papers already. There is a paper on trace formula for rank-1 groups (1974), and there are two papers on trace formula for general reductive groups (1978 & 1980). Also there is a paper in Corvallis Proceedings (1979), and a notes on trace formula (2005) which has become the standard introductory notes on this subject. I am seeking for any advice on how to read these references.


I wish to at least go through some details to feel how the formula is proved. Now I have read the notes by Whitehouse on trace formula for $\operatorname{GL}(2)$ (which covers a great many details about computation), and read a small part of Arthur's paper on rank-1 groups (1974). My question is that whether it is better to take 1974 paper first to gain more intuition, or instead start with the more general setting of reductive groups (like 1978 & 1980 papers), where maybe things are actually more clarified.


Any recommendation of other references is also sincerely welcomed. I am not aware of any other introductory references on trace formula on general reductive groups.


Thank you very much for reading this lengthy question! I am totally new to this community, so you are welcomed to point out any mistake.



How to read the paper of Arthur on trace formula on general reductive groups
One of the best places to learn about trace formula, other than David Whitehouse's wonderful notes, are the notes by Erez Lapid [Introductory notes on the trace formula](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.494.5118).


Arthur's trace formula relies on Langlands's work on Eisenstein series and Spectral decomposition from 1962–64. This stuff is extremely difficult for general reductive groups.


It would be near insanity to directly go to Arthur's papers or notes without mastering the spectral decomposition of automorphic forms on GL(2) and the Selberg trace formula. It is not wise to learn trace formula without learning about spectral decomposition.


For the general case, Borel's notes [Automorphic forms on reductive groups](http://homepages.math.uic.edu/%7Ertakloo/papers/borel/borel3.pdf) are a reasonable beginning.


My advisor Paul Garrett's book [Modern analysis of automorphic forms by example](https://www-users.cse.umn.edu/%7Egarrett/m/v/current_version.pdf) is, of course, my favorite place. They treat several examples, but do not do any higher rank case completely.


