I remember reading Weil's "Basic Number Theory" and giving up after a while. Now I find myself thinking of it(thanks to some comments by Ben Linowitz).

Right from the very beginning, Weil uses the fact that when you have a locally compact topolgocal group $G$ and a locally compact subgroup $H$, in addition to the Haar measures on $G$ and $H$, there exists a "Haar measure" on the coset space $G/H$, with some properties.

For instance, the upper half plane $\mathbb H$ is the quotient $SL_2(\mathbb R)/SO_2(\mathbb R)$ and the usual measure there which gives rise to the usual hyperbolic metric, is arising in this way.

I originally assumed this theorem and went ahead(but not much) with that book.

I want to have a reference for the above theorem. A reference which is not written by Weil. I find him very hard to penetrate. This should exclude Bourbaki's "Integration", as I supppose it would be heavily influenced by him, and thus is a horrible book(note to Harry: this is personal opinion; spare me the brickbats).

I had originally seen the construction of Haar measure on H. Royden's "Real Analysis", in which he is not considering any quotients.

Measure Theory? I have some vague recollections that a former officemate of mine went there to learn about exactly what you are asking about. $\endgroup$