I suggest Gelbart Lecture notes Arthur trace formula in addition to Gelbart Jacquet (Aakumadula`s r eferencereference).
Deitmar Echterhoff Principles of Harmonic analysisHere is good for a conceptual approachsite with references: (cocompact case only though). No detail ommitted.
There is also a long set of notes by Arthur and a LMN by Shokranian.http://www.charlesli.org/math/trace.html