2-dimensional galois representations Class field theory gives us a framework in which we can understand one-dimensional galois representations. I'd like to learn about the galois representations attached to modular forms, but I'm having trouble navigating the immense amount of material available on the web. Can someone give me a reference for the construction? Is this covered in Shimura's "Introduction to the arithmmetic theory of automorphic functions" book?
 A: Dear LMN,
No, the construction of Galois representations attached to modular forms is not covered in
Shimura's book. If you're a beginner in this field, then you need to know that the constructions for forms of weight $k=2$ predates the constructions for other weights 
($k>2$ and $k=1$) and is much easier -- though by no means simple. It is probably
better to learn first the case $k=2$, which is due to to Eichler and Shimura,
in some modern references, like the paper of Diamond, Darmon and Taylor on Fermat's last theorem, or the book of Diamond and Shurman on modular forms. For the case $k>2$, which needs a very solid knowledge of étale cohomology in addition to a command of the theory of modular forms, the original 1969 Bourbaki paper by Deligne stays an important reference.
Some alternative choices are given in the answers to this closely related question.
For the case $k=1$, read the original Annales de l'ENS paper by Deligne and Serre.
Now I would recommend that at the same time and even before you learn the actual construction of Deligne, you begin to learn how we use those Galois representations. Here the choices
of references and direction is almost infinite, but you may want to read Swinnerton-Dyer's paper on Ramanujan's congruences in Antwerpen, Modular functions of one variable III (in the Springer's collection that has the same initials as you, up to permutation), for an early and simple, but striking application.
