Note to the readerThis book has grown out of our endeavour to understand the theory of automorphic representations and the structure of Fourier expansions of automorphic forms with a particular emphasis on adelic methods and Eisenstein series. Our intention is also to open a path of communication between mathematicians and physicists, in particular string theorists, interested in these topics. Most of the results presented herein exist already in the literature and we benefitted greatly from [66, 98, 183-185, 297, 389, 405, 406]; our exposition differs, however, at places from the standard one. A few new results and examples are included as well; in particular, we provide many techniques for working out aspects of the Fourier expansion of Eisenstein series. We would be very grateful to learn of any omissions and mistakes that we have made unintentionally.Sections that are more advanced or explore topics beyond the main focus of this treatise are marked with an asterisk. discussions with colleagues both from the mathematics community and from the string theory community. We are especially indebted to