My long term goal for this "reading/study project" is to understand roughly what the Langlands conjectures are about. A more modest short term goal though, and more realistic one, is to understand:
1) the basics of Algebraic Number Theory, with a lot of examples worked out,
2) the basics of class field theory, but explained from a modern point of view, using adeles and ideles, eventually. However, I would like the abstraction to be gradual, so to speak, and motivated by a few worked out examples.
My background includes of course the usual Graduate Algebra courses, but I did read on my own quite a bit of commutative algebra and algebraic geometry. So I know what is a Noetherian ring, localization, the ring of integers in a number field, a UFD, a PID, the Galois group etc. I would like to know more about Dedekind domains and "onwards".
I would possibly like references that make analogies with algebraic geometry say, via schemes, for instance (I know the basics of schemes but I prefer an approach with many examples, kind of like, say, Eisenbud and Harris's book "The Geometry of Schemes", but with more examples worked out on the Algebraic Number Theory side).
I realize that my requirements may not all be met at once, but I will take whatever I can get, so to speak, in terms of advice and recommendations. Thank you!
I thank everybody for their comments. I have decided to use Milne's lecture notes http://jmilne.org/math/CourseNotes/index.html. I am starting with his algebraic number theory notes for now. It would take a while before getting to the Langland's program, but anyway, the process is fun. I appreciate more now the definition of Dedekind domains, which, from what I understand, took a while to formulate as the right setting for the rings of integers in number fields for instance (talking as a non-expert of course).
Edit: Neukirch's book is really nice by the way. I am now reading parts of it. Thank you @Mathmo123 for suggesting it, and I thank Prof. Khuri-Makdissi for also suggesting it (among others).