Many results in number theory are stated either in a classical language or in an adelic one. I am often impressed of the efficiency and the satisfactory computational properties of the adelic setting, often brief and well-behaved. They seems omnipresent, but barely justified, almost abstruse !
Unfortunately I never found a good reference book for the adeles and ideles definitions and properties : they always are treated in appendix or in a little chapter giving most of the time only the necessary stuff for the self-sufficientness ok the book.
Travelling among tens of lecture notes and books (Weil, Vignéras, Goldfeld, Lang, Milne, Tate, Bump, Gelbart, etc. : all books which have not adeles as main theme !) do not seem to be a good solution in order to have a good idea of adelic objects and properties : what are them ? for what do they exist ? are there examples and computation rules ? what are local and global properties ? splitting properties ? measures ? volumes ? general methods ? approximation theorems ? compactness of adelic groups ? are so many questions always only partially answered, often referring to an other book again...
So here is the question : is there any good reference, the more comprehensive possible, starting from the beginning and treating all the major aspects and properties of adeles, but not being just an arid handbook without intuition nor motivation nor examples ?